The Red Devils won the second leg 2-1 at home after extra time to take the tie into penalties, but lost the shootout 2-1 to the Black Cats.
"We didn't play well enough to merit going through," The Mirror quotes the Scot as saying. "Sunderland came here and deservedly got themselves in the final.
"In the end, I just don't think we got the level of performance we needed to get through the game. It went to penalties - and our penalties were terrible.
"Ideally, it wouldn't have been the group we had chosen. Javier [Hernandez] would have taken a penalty but was injured and people like Michael Carrick would have been involved."
Sunderland will take on Manchester City in the final of the competition at Wembley.