The Red Devils have slipped from champions to seventh in the Premier League table under new boss David Moyes as the transition from the 26-year tenure of Sir Alex Ferguson continues at the club.
Mata says he knew what he was getting into when he became the club's record transfer with his switch from Chelsea in January, and Moyes must be given time.
The Spanish ace told the Daily Mirror: "We have to be together. Now is not the time to blame anyone. Now is not the time to look for guilty people.
"Now is the time to stick together - with the manager, with his staff, the players and with the people on the board of the club. We need to carry on, to stay with the manager. We need to believe in him, because as players we know we have to improve.
"It's not just the manager, it's not just the tactics. It's all of us. It's not the time to blame one person. We are all together in this.
"Some of my friends told me if this situation was happening in another club in Spain it would be different, but the club and the players are behind the manager.
"We need to be strong as a team, as a dressing-room and keep working hard. We need to improve, we know it, but we need to do it together."
He added: "I knew these six months were going to be difficult. Even before I came, things were difficult here, so I knew I wasn't coming to a side that was going to win, win and win.
"But I knew as well that this club was going to come back and that the future was going to be bright."
Mata has backed Moyes to bring in the right players in the summer to make sure the club will challenge for trophies again next season.
"I have no doubt about it. When I joined, in all my conversations with the board and the manager about next season, they were confident about getting the right players," he said.
"They know, and I know, we're in a transitional moment, but in the summer they're going to try to sign a few players and I have the faith they are going to bring top players in.
"I'm sure this club is going to come back and fight for every trophy. Since I was a kid, Manchester United was fighting for everything, and this moment is going to come back for sure.
"The club is in a transitional moment. They had Sir Alex Ferguson as the manager for the last 26 years, so I think it's a big change for the club.
"I don't know how many clubs in the world that have had the same manager for nearly 30 years - probably none. That was a unique situation.
"But we have to look forward to the future, and I have to say I think the future for this club will be bright, because it deserves the best."