The Spanish side booked their place in the quarter-finals of the competition on a controversial night at Old Trafford as their 10-man hosts could not hold onto the lead given to them by Sergio Ramos' own goal.
Luka Modric and Cristiano Ronaldo struck in quick succession for the visitors to claim a 3-2 aggregate victory after Nani was dismissed by Turkish referee Cuneyt Cakir for a high challenge on Alvaro Arbeloa, although the winger's eyes were on the ball and not the man.
Mourinho told Sky Sports: "Manchester United were playing very well. They were very compact, they were very aggressive, very well organised technically and the match was very difficult for us.
"I doubt with 11 against 11 we could win the match.
"I had a feeling that Modric would change the match because he brought to the game some qualities that we did not have on the pitch at the time.
"I am a bit frustrated because we played so well against Barcelona and today I was waiting for more. I know they (Manchester United) are giants, not just physically but mentally. I know they are fantastic and have a manager capable of organising and motivating people.
"But I was waiting for us to come here and play in a different way."
Former Chelsea boss Mourinho again insisted he would be happy to return to the Premier League in the future, with his tenure in Madrid tipped to come to an end in the summer.
He added: "Everyone knows I love it, and everybody knows one day I will be back, that's for sure, unless nobody wants me! But if somebody wants me one day I have to be back because I enjoy it so much."