Portsmouth, who have won the FA Cup once in their history, in 1939, were made favourites for the competition after surprising Premier League champions Manchester United on Saturday.
The Baggies have won the cup five times but not since 1968.
Barnsley, who are struggling in the bottom half of the Championship, are making their first appearance in the last four since 1912.
Welsh side Cardiff, for whom the cup run is a welcome distraction from financial problems, won the cup in 1927.
The semi-final line-up ensures a first winner from outside the game's current 'big four' of Arsenal, Manchester United, Liverpool and Chelsea since 1995.
Barnsley chairman Gordon Shepherd has revealed the Tykes' fairytale FA Cup run will earn the club £2.6million if they can overcome Cardiff in the last four.
Shepherd said: 'We've probably made up to now, with winners' bonuses so far and gate receipts and things, around £1million.
'We think once we've played the semi-final it will probably be worth another £700,000.
'However, if we won the semi-final we'd get a £900,000 winners' bonus as well, so there's a lot at stake, there really is.
'A club like this can always use money because we don't generate a great deal of revenue. We have average crowds of 10,000, so we actually we do need the money just to continue.'
An estimated 33,000 Tykes fans will converge on Wembley for the semi-final clash over the weekend of April 5/6, with a similar number expected should they make it all the way to the final for the first time since 1912 - the year the Titanic sunk.
Davey attempted to shift his side's focus to Tuesday's league match with play-off chasing Ipswich at Oakwell, but conceded he had only just returned from dreamland.
The manager, whose side lie in 19th place in the table, four points clear of the relegation zone, said: 'I had a day and a half on cloud nine, but we've got to prepare for a big game tomorrow against Ipswich.
'So that's the main priority now, to get all the press out of the stadium and start focusing on the game tomorrow night.
'But it's fantastic. To be a manager in my first full season, to be able to lead a team out at Wembley.
'I've listened to Harry Redknapp and he's not led a team out at Wembley in the all years he's been a manager, so for me to do it in my first year is a great achievement.
'It might never come again, so I'm going to relish every moment of it.'
Davey added: 'I think any of the four teams can win it now. There's no big-six clubs. The Liverpools, the Chelseas, the Man Uniteds, the Arsenals, the Tottenhams, the Evertons are all out.
'And that's a testament to Championship clubs - three of them in the last four and all three teams outside the Premier League will think they have a chance of winning it.'
Meanwhile, goalkeeper Luke Steele, on an emergency month-to-month loan spell from West Brom, breathed a huge sigh of relief when Barnsley avoided the Baggies in the draw.
Steele, whose heroics at Anfield in his first match for the Tykes earned him the FA's player-of-the-round award, would not have been eligible to face his parent club in the last four.
Davey said: 'We're pleased for him. He's worked very hard since he's come here and he's put in some fantastic performances.
'He's played the last two rounds for us and for us not to draw West Brom solves a problem, and now he'll be available to play. We just hope he doesn't get injured.
'We're in the process of talks now with West Brom to see if we can get him until the end of the season. That's the plan and we'll hear in the next couple of days.'
Cardiff boss Dave Jones is expecting a close battle between the Championship rivals, who are separated by only two points in the table.
'We've got a tough one,' he said. 'We said that in the last round and the round before. We'll know each other inside out. Hopefully we'll come out on top but I'm sure Simon will be thinking the same.
'Anybody you play in our division is a tough battle. They've come off the back of two fantastic victories so they won't fear anyone. We played well yesterday and we're looking forward to it.'
There have been claims there will be less interest in the semi-finals and final because none of the big teams are involved, but Jones thinks it is a shot in the arm for the competition.
'Everyone talks about the romance of the cup,' he said. 'Year in, year out it is always the same teams that seem to be playing but this time around it's probably the year of the underdog.
'At the moment it looks like Pompey will be the favourites and we'll be vying for a spot against them but I'm sure West Brom will have a lot to say about that, and you never know because of the results that have gone before.'
Manchester United boss Sir Alex Ferguson criticised the choice of Wembley to stage the semi-finals but Jones believes it is an added bonus for the three Championship sides.
'Everyone wants to play a final at Wembley but for the likes of us to go there in a semi-final is fantastic for us. It does give an added little bit of romance and spice to it,' he added.
The four clubs are potentially two wins away from European football but Cardiff will not be able to claim their spot in the UEFA Cup should they win the final because they represent the Football Association of Wales.
But City chairman Peter Ridsdale, who previously owned Barnsley, hinted the club might be prepared to challenge that.
He said: 'If we win the final and we're not put forward to the UEFA Cup I'm sure there'll be a lot of people with something to say.'
Portsmouth chief executive Peter Storrie was pleased with the outcome of the draw despite landing the highest-placed of the other three teams.
Storrie said: 'We've got to be beat two of the three semi-finalists to win the cup so we have to take it as it comes. After Manchester United we can't fear anybody.
'It is unusual. On Saturday morning we were driving to Old Trafford thinking it was going to be the Alamo. Now we are 5-4 favourites - it's a funny old game, football.
'I have been in the game 20 years and this is one of the greatest results of my career.
'It was a good performance from the team and it is still pretty hard to take in.'
Storrie also had words of praise for manager Harry Redknapp, who was tempted to move to Newcastle in January but opted to stay at Fratton Park.
He added: 'I think Harry had an opportunity to go to a big club. He always wanted that chance but felt a lot was still to happen from us.
'If we can go on and win the FA Cup it will be a great testimony to his decision.'
The Baggies have won the cup five times but not since 1968.
Barnsley, who are struggling in the bottom half of the Championship, are making their first appearance in the last four since 1912.
Welsh side Cardiff, for whom the cup run is a welcome distraction from financial problems, won the cup in 1927.
The semi-final line-up ensures a first winner from outside the game's current 'big four' of Arsenal, Manchester United, Liverpool and Chelsea since 1995.
Barnsley chairman Gordon Shepherd has revealed the Tykes' fairytale FA Cup run will earn the club £2.6million if they can overcome Cardiff in the last four.
Shepherd said: 'We've probably made up to now, with winners' bonuses so far and gate receipts and things, around £1million.
'We think once we've played the semi-final it will probably be worth another £700,000.
'However, if we won the semi-final we'd get a £900,000 winners' bonus as well, so there's a lot at stake, there really is.
'A club like this can always use money because we don't generate a great deal of revenue. We have average crowds of 10,000, so we actually we do need the money just to continue.'
An estimated 33,000 Tykes fans will converge on Wembley for the semi-final clash over the weekend of April 5/6, with a similar number expected should they make it all the way to the final for the first time since 1912 - the year the Titanic sunk.
Davey attempted to shift his side's focus to Tuesday's league match with play-off chasing Ipswich at Oakwell, but conceded he had only just returned from dreamland.
The manager, whose side lie in 19th place in the table, four points clear of the relegation zone, said: 'I had a day and a half on cloud nine, but we've got to prepare for a big game tomorrow against Ipswich.
'So that's the main priority now, to get all the press out of the stadium and start focusing on the game tomorrow night.
'But it's fantastic. To be a manager in my first full season, to be able to lead a team out at Wembley.
'I've listened to Harry Redknapp and he's not led a team out at Wembley in the all years he's been a manager, so for me to do it in my first year is a great achievement.
'It might never come again, so I'm going to relish every moment of it.'
Davey added: 'I think any of the four teams can win it now. There's no big-six clubs. The Liverpools, the Chelseas, the Man Uniteds, the Arsenals, the Tottenhams, the Evertons are all out.
'And that's a testament to Championship clubs - three of them in the last four and all three teams outside the Premier League will think they have a chance of winning it.'
Meanwhile, goalkeeper Luke Steele, on an emergency month-to-month loan spell from West Brom, breathed a huge sigh of relief when Barnsley avoided the Baggies in the draw.
Steele, whose heroics at Anfield in his first match for the Tykes earned him the FA's player-of-the-round award, would not have been eligible to face his parent club in the last four.
Davey said: 'We're pleased for him. He's worked very hard since he's come here and he's put in some fantastic performances.
'He's played the last two rounds for us and for us not to draw West Brom solves a problem, and now he'll be available to play. We just hope he doesn't get injured.
'We're in the process of talks now with West Brom to see if we can get him until the end of the season. That's the plan and we'll hear in the next couple of days.'
Cardiff boss Dave Jones is expecting a close battle between the Championship rivals, who are separated by only two points in the table.
'We've got a tough one,' he said. 'We said that in the last round and the round before. We'll know each other inside out. Hopefully we'll come out on top but I'm sure Simon will be thinking the same.
'Anybody you play in our division is a tough battle. They've come off the back of two fantastic victories so they won't fear anyone. We played well yesterday and we're looking forward to it.'
There have been claims there will be less interest in the semi-finals and final because none of the big teams are involved, but Jones thinks it is a shot in the arm for the competition.
'Everyone talks about the romance of the cup,' he said. 'Year in, year out it is always the same teams that seem to be playing but this time around it's probably the year of the underdog.
'At the moment it looks like Pompey will be the favourites and we'll be vying for a spot against them but I'm sure West Brom will have a lot to say about that, and you never know because of the results that have gone before.'
Manchester United boss Sir Alex Ferguson criticised the choice of Wembley to stage the semi-finals but Jones believes it is an added bonus for the three Championship sides.
'Everyone wants to play a final at Wembley but for the likes of us to go there in a semi-final is fantastic for us. It does give an added little bit of romance and spice to it,' he added.
The four clubs are potentially two wins away from European football but Cardiff will not be able to claim their spot in the UEFA Cup should they win the final because they represent the Football Association of Wales.
But City chairman Peter Ridsdale, who previously owned Barnsley, hinted the club might be prepared to challenge that.
He said: 'If we win the final and we're not put forward to the UEFA Cup I'm sure there'll be a lot of people with something to say.'
Portsmouth chief executive Peter Storrie was pleased with the outcome of the draw despite landing the highest-placed of the other three teams.
Storrie said: 'We've got to be beat two of the three semi-finalists to win the cup so we have to take it as it comes. After Manchester United we can't fear anybody.
'It is unusual. On Saturday morning we were driving to Old Trafford thinking it was going to be the Alamo. Now we are 5-4 favourites - it's a funny old game, football.
'I have been in the game 20 years and this is one of the greatest results of my career.
'It was a good performance from the team and it is still pretty hard to take in.'
Storrie also had words of praise for manager Harry Redknapp, who was tempted to move to Newcastle in January but opted to stay at Fratton Park.
He added: 'I think Harry had an opportunity to go to a big club. He always wanted that chance but felt a lot was still to happen from us.
'If we can go on and win the FA Cup it will be a great testimony to his decision.'
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