Skipper Nemanja Vidic admitted his side were beaten by the better team.
"I think if you look at it we have never played a team in the past like Barcelona, they played good football and deserved to win," he told ITV.
"We tried to press high and in some parts of the game we did well. The goals we lost, we didn't do what we have to do to close their players down. When they have time on the ball they can make the final pass and that is what they did."
Vidic's defensive partner Rio Ferdinand concurred with his skipper's view that United were second best against the four-time winners.
"We gave it a better shot this time than last time (in Rome in 2009), we had a couple of opportunities," he told Sky Sports.
"We got back in it at 1-1 and thought we could come back and win but it wasn't to be, we have to give them credit.
"A couple of the goals were preventable but you have to give credit where it's due. They've got a system they work to and did it well. We had a game plan we thought could beat them, but wasn't to be."