The Manchester United manager has suggested that the Blues missed a big opportunity to progress to Wembley and is confident his side will not suffer from the same tiredness again
The Red Devils took a 2-0 lead in the original tie but Chelsea scored twice after half-time as United tired following their midweek Champions League tie against Real Madrid.
Sir Alex's team will travel to west London on Monday to play for a semi-final fixture against Manchester City and the 71-year-old has warned that they will be in better shape this time around.
"I thought we were lucky to be honest with you," he told reporters. "I think that tiredness had got into some parts of the team.
"And from a comfortable position for the first 20 minutes you could see us before half-time that we started giving the ball away and that is a definite sign of tiredness.
"I think the tiredness possibly came from the emotional intensity of the Real Madrid game and also the way in which we lost it.
"I think it affected two or three players in the second half - Tom Cleverley in particular - and our two full-backs' legs had gone.
"I think that was down to emotion because the way our full-backs are they put so much energy into going forward they find it difficult going back.
"That made it a long game against Chelsea and they had the advantage of having extra midfield players in their team.
"They really deserved to win the game in the second half. David de Gea's save [from Juan Mata in the closing stages] was one thing, but also we were scrambling about to just get through the game.
"But we're fresher now and we have a strong squad in terms of picking two teams."
Chelsea have won the FA Cup four times since United last lifted the trophy by beating Millwall at the end of the 2003-04 campaign.
Sir Alex shrugged off the Blues' superior recent record, however, as the product of the seven-times winners having been handed easier routes to the final in recent years.
"They have a good record, but we try to win it every year," he insisted. "The last few seasons we've had some very difficult draws.
"I think Chelsea have enjoyed the benefit of home draws over the past few years and I don't think they have had one hard game in their run to semi-finals over the years.
"And that helps, there's no doubt about that. But they have us to play and Stamford Bridge won't be easy."
With Robin van Persie's barren spell now stretching to eight club matches after he completed 90 minutes against Sunderland on Saturday, Chicharito is likely to lead the line for United.
"Yes, Chicharito is likely to play," Sir Alex confirmed. "He's got a great scoring record against Chelsea."