With United holding a 1-0 lead from the first leg at Stamford Bridge, Javier Hernandez crashed home the night's opening goal just before half-time from Giggs' cross. When Ramires was dismissed for the Blues in the 70th minute, their hopes seemed all-but over.
However, substitute Didier Drogba reduced the deficit in the 77th minute before Ji-Sung Park immediately went up the other end to reclaim United's two-goal cushion and end the contest as United won 3-1 on aggregate.
Ferguson told Sky Sports: "I think we played very, very well against a very, very good team. Chelsea played a big part in that game today.
"I thought we were the better team on the night. In a team game. we had some fantastic performances: Park, Chicharito (Hernandez) - all over. No-one let us down."
Ferguson admitted his side were lucky to score so quickly after Chelsea's leveller on the night. "That was the break we got in the game, to be honest. I thought it was a cheap goal to lose.''
Chelsea manager Carlo Ancelotti was gracious in defeat. "We had control of the game for the first 25 minutes but were not able to score,'' he said. "At the end of the first half when they scored it was more difficult for us, we came back with 10 men but in the end it was not enough.
"Our performance was not so bad but I think of the two teams, Manchester United deserved to win.''
Ancelotti praised Drogba's impact from the bench but side-stepped the question of whether he regretted starting with Fernando Torres instead. Asked about the task of lifting his team, the Italian said: "It will be difficult but we have to make the top four for Champions League football next season.
"We need to quickly move on from this defeat, this disappointment, and onto the next game.'' As for Torres, he added: "We have to believe (in him), we have to wait until he improves.''
"We expected them to come at us. They needed to score; we knew we needed to try to score too, to take the pressure of us. I think we deserved it. We played well down there, had a good gameplan and stuck to it and tonight got a couple of great goals.
"The second goal came at exactly the right time. They had just scored, so us scoring so quickly after they had knocked the stuffing out of them, really."