United ended its season in uninspiring fashion on Monday (NZST), losing 2-0 at home to relegated Cardiff City to finish sixth in the Premier League, 32 points behind bitter rival Manchester City, which retained its title.
Writing in his weekly blog, Mata conceded United have badly underperformed since an initial strong success under Jose Mourinho's successor as manager, Ole Gunnar Solskjaer.
United failed to win any of their last six games of the season in all competitions and managed just two victories after a stunning last-16 Champions League comeback against Paris Saint-Germain in March.
"The season has come to an end in England and obviously we head into the summer break disappointed," wrote Mata.
"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.
"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 will last the whole summer.
"All of you, however, have been way better than the team. When I see your faces at Old Trafford, applauding, supporting and cheering us on after waiting for ages to say goodbye to us, I understand how big this sport is… and how big this club is. You all deserve a lot more than what you're getting. That is the reality."
Mata, 31, is yet to agree a new contract at Old Trafford and his future is very much in doubt, with his deal expiring at the end of June.
United has already lost two of its longest-serving players, with Antonio Valencia and Ander Herrera set to depart before 2019-2020.
"This weekend we said goodbye to Antonio Valencia and Ander Herrera as Red Devils," Mata wrote.
"Two players and two friends who I have shared a lot of experiences with both on and off the pitch.
"Our fans gave them a heartfelt goodbye as was expected, because the two have given a lot to this club."