The Red Devils headed to Valencia on Wednesday already assured of progression to the knockout stage.
Defeat for the Bianconeri meant that United could snatch first place with a win at the Mestalla, but they also slipped to a 2-1 reversal and now face the threat of being paired with the likes of Real Madrid, Barcelona, Bayern Munich and Paris Saint-Germain.
“We are disappointed because obviously it's more painful knowing that Juventus lost and if we'd have won we would have finished first in the group,” former Valencia midfielder Mata told reporters after a return to familiar surroundings.
“It’s a disappointing night. It was special for me personally coming back to Valencia and feel the love of the club and the supporters, so I am grateful for that.
“But I’m disappointed overall. I think we reacted a bit too late, so we had some chances at the end that we could have scored.
“But overall we qualified and that was the most important thing and we knew that, but obviously we would have loved to have been first in the group.”
Having failed to emerge victorious on midweek European duty, United are now stumbling towards a crunch Premier League clash with leaders Liverpool on Sunday.
Mata concedes that things are not getting any easier for Jose Mourinho’s side, telling MUTV: “It's a very busy month and we have very important games coming, especially on Sunday.
“But I don't think it's an excuse because as a football player, you focus on the game that you are playing and try to give your best in every single game.
“Today we were already qualified but it was still a Champions League game against a good team.
“Obviously, they wanted to show that they can beat a club like Manchester United and they are not in a very good position in the league either.
“But they pushed, and they wanted to show they are a very competitive side.
“I know it's difficult, but we have to keep going and especially with what we have coming on Sunday, we need to be ready for that.”