United have been working hard in a bid to be fully prepared for the new campaign after manager Ole Gunnar Solskjaer was left disappointed by the fitness levels of his players when he replaced Jose Mourinho.
Speaking to MUTV, Mata said: "To be honest, we've been training quite hard.
"The first two-and-a-half weeks were quite physically tougher than last season. Obviously, the results have been better also, winning every single game.
"But I think it's good also for Ole and for his staff to have a full pre-season where we can play the way he wants us to play.
"We have time to train our patterns a little bit, we have time to train tactically [and] physically, so I think it's been good."
He added: "I think the manager said it not long ago. The atmosphere is very good. We have very nice people in the dressing room, everyone trying to help.
"Everyone [is] demanding from each other, which is what I think we need to do in a club like Manchester United.
"In every single training we have to set higher standards; that's the only way to compete and we know we have to do that."