United conceded an injury-time penalty when Nani lost possession and 21-year-old Scott Wootton brought down Ramires, allowing Eden Hazard to make it 3-3.
Wootton was then guilty of a poor header in extra time that allowed Daniel Sturridge to score as Chelsea avenged their 3-2 loss to the same opposition in the Premier League on Sunday.
Ferguson was unafraid to criticise Wootton or his fellow centre-back, 19-year-old Michael Keane, while Nani was also targeted by the United boss.
"We have done fantastically well and I think we have thrown the game away really," Ferguson told BBC Sport.
"With the game finished, we had possession of the ball around about the corner flag and Nani decides to beat a player and we've lost a penalty kick.
"We didn't deserve it but in extra-time I think they found it too much in terms of the young players.
"You can always play young forwards because they don't cost you the game but young centre-backs have to be really top drawer at this level of football.
"Wootton is 21 years of age, Michael Keane is 19 years of age, obviously they will learn. It's a sore lesson from them in that respect - getting knocked out of the cup.
"We have good options in attack, but obviously losing five goals in a game of football, then you have to worried about that."
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