Red Devils skipper Ryan Giggs put his side ahead in the 22nd-minute when he capitalised on a Chelsea lapse in defence before David Luiz restored parity from the penalty spot.
Javier Hernández produced a clinical finish just before half-time, but once again, the Blues levelled after Gary Cahill directed a thunderous header past Anders Lindegaard.
Nani appeared to have scored the winner in the 59th minute to seal United’s passage to the last eight, but Eden Hazard scored from the spot in added time to give Chelsea a dramatic equaliser and force an additional 30 minutes.
And Di Matteo’s men set up a quarter-final tie against Leeds United courtesy of extra-time goals from Daniel Sturridge and Ramires, with Giggs netting a consolation strike from the spot.
“We were playing really good football at 3-2 up and all we needed to do was keep the ball,” said Ferguson.
“But Nani decided to beat a player, we lost the ball, and it ended up in a penalty kick against us.
“I don’t know was it a penalty or not, but at that point, our young players started to feel it and it was very difficult in extra-time.”
He added: “We had control of the game. They had a lot of attacks but nothing really came of them and our counter-attack was really good.
“But if you’re winning 3-2 in the final seconds of the game, you really should see the victory out.”
Ferguson was particularly annoyed by Nani’s loss of possession in the lead up to Scott Wootton’s foul on Ramires which resulted in Hazard’s leveller in the 90th minute.
“He’s experienced and he’s an individual and he’s a player who wants to beat men – and we’re not going to discourage him from that,” added Ferguson.
“But in that situation, if he had kept the ball in the corner flag, the game is over.”
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