The Premier League leaders threw away a two-goal lead to draw 2-2 with the London club in the quarter-finals on Sunday and will now have to travel to Stamford Bridge for a replay.
And Ferguson, who has been accused by Chelsea counterpart Rafa Benitez of snubbing a pre-match handshake, thinks the midweek defeat by Real Madrid took a lot out of his players.
"We're lucky to still be in the cup," the Scot told MUTV. "We just ran out of legs and Chelsea were far the better team in the second half.
"But I can't be critical of my side, because the running they had to do on Tuesday night, against a really top side in Real Madrid, had its bearing on today's result, no doubt about that.
"The two full-backs, Rafael and Patrice [Evra], are knackered and the two central midfielders tired badly.
"We kept giving the ball away and it made it a long day for us, going from one penalty box and back to our own."
Chelsea had played away against Steaua Bucharest on Thursday evening, suffering a 1-0 first-leg defeat in the last 16 of the Europa League.
United were better in the first, Chelsea in the second. But on balance of play, I'd say Chelsea's half was stronger than ours. Were it not De Gea, we'd be staring at a second cup exit inside 5 days.- HarryBoulton