The Red Devils were expected to get past the already relegated side with ease but a lack of intent and purpose saw Cardiff getting the better off the English giants.
United’s failure to win this game meant there will be no Champions League football next season and Ole Gunnar Solskjaer’s side will be competing in the Europa League.
Mata’s contract is set to expire at the end of this season and the Spaniard could be the third player after Ander Herrera and Antonio Valencia as he is yet to take a decision on his future.
Mata said, “A defeat on the Premier League’s final weekend was the worst way to finish off what hasn’t been a good campaign for anyone who is part of the Manchester United family.
“There have been some good moments and matches along the way, which have to be remembered, but the feeling, in the end, is very bitter.
“None of us are satisfied with the general performance levels that we have offered, for one reason or another. When we win, we do so together, and when we lose we also share the responsibility.
“Now is the moment to analyse, reflect and improve, because this club should be in a different situation to the one we find ourselves in, there can be no doubt about that.
“Although it isn’t healthy to just focus on the negatives, it also isn’t possible to deny the obvious. We have to be realistic and the season has been very disappointing.
“It’s very painful and that feeling will last through the whole summer. You all deserve a lot more than what you’re getting. That is the reality.”