Javier Hernandez and Park Ji-sung gave United a 3-1 aggregate win after substitute Didier Drogba equalised on the night for 10-man Chelsea, who had Ramires sent off in the second half.
Defeat means Carlo Ancelotti's side are likely to finish the season empty-handed and leaves the Italian with his job on the line.
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Ancelotti later admitted he may have blundered by starting with ?50million striker Fernando Torres, who was substituted at half-time after failing to score for the 11th game.
Ferguson, who was taking charge of his 100th European game at Old Trafford, paid tribute to Ryan Giggs who set up both of United's goals, saying: 'He's incredible a unique person and player. His contribution is big because of the goal he set up in the first game, and the part he played in the goals tonight. To play at 37 requires tremendous sacrifice.'
Drogba, a half-time replacement for Torres, cancelled out Hernandez's goal after 76 minutes but United were ahead again through Park 21 seconds later.
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Ferguson added: 'That was the break we got in the game, to be honest. It was a stupid goal for us to lose and we had to respond quickly. Park's record in big games is fantastic.
'We played very well against a very good team. Even with 10 men they had a go and credit to them, but I thought we were the better team on the night.'
Questioned about winning the Treble as United prepare for Saturday's FA Cup semi-final with Manchester City, Ferguson said: 'I keep being asked about it but you need luck to do that. Saturday is a massive game.
'Momentum is a great thing and everybody is desperate to play in every game. They're desperate to play against City on Saturday.'
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United are now set for a likely semi-final meeting with Schalke.
Ancelotti insisted he does not fear for his future following Chelsea's latest European failure. He said: 'I'm not concerned. I have to work. I have to try to do my best. It's not my decision whether I stay or not here. I haven't spoken with him (Roman Abramovich).'
Asked if it was a mistake to start with Torres rather than Drogba, he added: 'Maybe. Could be. But I thought a long time to take this decision. I preferred to start with Fernando for this kind of game, with these kind of tactics. Didier played very well in the second half.'
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