The previous year Arsenal and Tottenham drew each other in one semi- final and the two Sheffields in the other. The clamour to stage both matches at Wembley was irresistible, especially as the precedent had been set by Arsenal and Tottenham in the semi-final in 1991. Both 1994 matches were then scheduled for Wembley, but with not quite the same justification.
So while Manchester United and Oldham Athletic were booked in for the Sunday, Pleat's modest Luton side, then lying 18th in the First Division, found themselves thrust into a match against Chelsea on the Saturday on the biggest stage of all. They lost 2-0, but worse for Pleat than the team's performance - which actually wasn't at all bad - was everything that surrounded the occasion.
"It was crazy," Pleat recalled last week. "People were treating the match like it was the Cup final. It should never have been played at Wembley. OK, so it was the semi-final, but it went to people's heads. There were arguments among the directors about tickets for the Royal Box. There was a big fuss about the pre-match press conference. I picked the wrong hotel. It all went drastically wrong."
Somehow one can't see that happening should Pleat return to Wembley in a couple of months' time with a Sheffield Wednesday team who take on Wimbledon in today's quarter-final, and not just because Wednesday only have to go back four years to their last final, when they lost in a replay to Arsenal.
Wednesday have been the quietest success story of the season. They are about as starry as a cloudy sky, but thanks in large part to Pleat's combination of astuteness and undying enthusiasm, they have turned into one of the most consistent teams in the Premiership, extremely tough to beat, and a Uefa Cup place is a very realistic aim.
A solitary defeat in their last 22 games tells its own story. They may have drawn more games than any other Premiership team (12 out of 28) but such a ticking over engenders a deep-seated confidence. And to be coming into the quarter-final on the back of last week's emphatic 3-0 win at Nottingham Forest may give them a slight advantage over a Wimbledon side who with a defeat and a draw in their last two matches appear to be going slightly off the boil. The teams' Premiership records are almost identical, Wednesday having 45 points from 28 games, Wimbledon 44 from 27.
When they met at Selhurst Park earlier in the season, Wimbledon won 4- 2, but only after Wednesday had missed a penalty with the score at 3-2. "It wasn't a true reflection of the match, but then against Wimbledon it often isn't in terms of possession," Pleat said. "They play in a straightforward, expedient way and don't make too many passes. Even though their type of game has changed a little bit, it hasn't changed drastically."
The key to Wimbledon, Pleat thinks, is the front pairing of Efan Ekoku and Marcus Gayle. "They carry the team." So after the successes Pleat enjoyed when his team came up against Steve McManaman and Gianfranco Zola earlier this season, are we going to see him deploy man-markers this afternoon? "Not necessarily," he said. "They play far enough up for them to be marked naturally."
Either way it promises to be a fascinating tactical battle between two of the cleverest and most resourceful managerial brains in the country. Pleat and Joe Kinnear are the same generation - aged 52 and 50 respectively - and they have both built reputations making a little go a long way, Pleat at Luton in the early 1980s, Kinnear more recently at Wimbledon. But unlike Kinnear the football played by Pleat's teams has always been based on keeping the ball.
Never has Pleat's stock been higher than in that outstanding season he had at Tottenham when they not only got to the FA Cup final but also to the semi- finals of the League Cup, and finished third in the old First Division. With a five-man midfield that included Glenn Hoddle, Chris Waddle and Ossie Ardiles, and the 49-goal front man in Clive Allen, Pleat fashioned one of the most attractive and effective club sides of recent times. He won't consider them in the same breath as his Wednesday team. "There are no comparisons at all," he said. "It's difficult to compare eras. I'd like to think there was, but we're not as talented as Tottenham were."
Wednesday have their strengths, none the less - from Kevin Pressman in goal, through Des Walker at the back, the marker supreme in Peter Atherton, the cultured left foot of Mark Pembridge in midfield, David Hirst up front, and the attacking flair of Regi Blinker and Benito Carbone.
"We're well balanced," Pleat said. "We can produce a little bit of pace in some areas but lack it in others. We're very good at retrieving possession. I'd like to think we were better at keeping the ball, but we're always looking to get it back." As with Wimbledon, the collective approach is everything. Since arriving at Wednesday from a second spell at Luton in 1995, Pleat says he has "completely knocked on the head" the idea of individuals being bigger than the team.
Pleat has never been one to glorify himself any more than he does any of his players. He remains one of the most natural and approachable managers, a tremendous talker on the subject, often intensely so, but what he says is always worth listening to. Underneath a romantic spirit is at work. He cherishes the memory of the Matthews final of 1953 - he was eight at the time - of his boyhood hero John Charles, and of seeing the Tottenham Double side at their best.
The game is in his heart as much as his head. "The pleasure of winning is very short compared with the disappointment of losing, which seems to last for ever. You can't escape it. You feel a sense of guilt. It's a terrible feeling." Hence the drive to succeed. "My son gave me some golf clubs, but I haven't used them. I feel if I'm doing my job properly I'm better off at a match."
Pleat is a traditionalist in many ways. He worries that television may be taking over the game. "Where's the next generation of players coming from? Not from sitting in front of Sky." Some of the magic of the Cup has gone when the quarter-finals are split up over two days. So does that mean winning would matter less to him this year than it would have done 10 years ago? "Of course not!"
And does he have an inkling that it might just be Wednesday's year? "I think it's dangerous to have special feelings about it," he said. "But I just feel that the way we're playing it will take a good side to beat us."
Judgement day: Verdict on today's FA Cup quarter-finals by Ian Ridley
Sheffield Wednesday v Wimbledon
Wimbledon deserve something from their season but it may be that the Coca-Cola Cup, in which they play Leicester City in a semi-final second leg at home on Tuesday, represents the better chance of a Wembley appearance. Wednesday go into the match in excellent form with, crucially, a defence at its niggardly best thanks to Kevin Pressman and Des Walker. In midfield, Mark Pembridge should ensure that Wednesday are not outfought by Vinnie Jones and Co, while Benito Carbone's tussle with Chris Perry will be intriguing. David Pleat took Tottenham to the final 10 years ago; for him it would apt reward if what goes around comes around. Forecast: 2-1.
Portsmouth v Chelsea
Gianfranco Zola is exhausted, according to reports out of Chelsea. We'll believe it when we see it. How much energy does it take, anyway, to curl home a free-kick from 25 yards? One such moment could ruin all the tactical nuances, with Terry Venables having swapped his owner's office for the training ground to help Terry Fenwick find an antidote to Ruud Gullit's manoeuvrings. Much will depend on how Pompey counter Dan Petrescu on the right and how much pressure they can exert on Franck Leboeuf as instigator of attacks and defensive co-ordinator. Lee Bradbury and Mathias Svensson have it in them. Forecast: 1-1 (Chelsea destined - after that penalty - to win replay).
Chesterfield v Wrexham
"Blues for the Cup, Reds for the election," says Chesterfield's MP Tony Benn. But if it happens, that spire will surely straighten; Chesterfield winning the Cup, that is. There appears little to choose between these two mid-table Second Division teams who have added flavour to the competition but on the evidence of impressive away wins at West Ham and Birmingham City, Wrexham look to have the edge over a Chesterfield side who got lucky against a feeble Nottingham Forest and who will be without two key players as a result of that brawl with Plymouth Argyle, Kevin Davies and Darren Carr. In Kevin Russell, Wrexham may have the match-winner. Forecast: 0- 1.