Current Ajax boss, Ten Hag, will swap Amsterdam for Manchester in the summer as the Old Trafford club make their latest overhaul in an ongoing quest to return to the pinnacle of the sport.
The Red Devils are set to miss out on Champions League qualification with the club currently down in sixth place, five points away from fourth-placed Arsenal.
Mata, who might not be handed a new contract once the current one expires in the summer, recognised the current frustrations but believes the club will head in an exciting direction under Ten Hag.
He said: "I understand the fans' frustration after this season because I would also be frustrated too," Mata told United's official club website.
"But I also think there is an exciting future ahead, with a new era, with a new manager.
"Hopefully it is going to be a big change in terms of results and fans will be happy."
United take on Brentford on Monday, but with the top four seemingly beyond their reach, there have been question marks over the team's motivation.
Mata challenged his teammates to deliver the right attitude and fight until the end, saying: "Whenever you step onto that pitch it's always special. Hopefully we can have a good game, we can end this season at home on a positive note because that's what the fans deserve.
"Every single game that you play for this club you can play better or worse, you can have better or worse results but as a fan the thing I would like to see is players giving everything and fighting together and representing the club the best we can.
"That's what we have to do unfortunately in the next [three] games because there are no more.
"Like I say, it is a question of pride and giving to the club what it deserves from us."