Van Gaal has enjoyed a positive to start to life with United, overseeing friendly wins in his opening two games against LA Galaxy and Roma as part of their pre-season tour of America.
The 62-year-old guided the Netherlands to an impressive third-place finish at the World Cup earlier this summer, and now faces the task of leading his new side to an improvement upon their disappointing Premier League campaign.
United slumped to a seventh-place finish under Moyes – their lowest since 1990 – but Mata believes that van Gaal is already showing signs of being able to change their fortunes during a tough training camp.
"He is right to be demanding. As a player you want a coach like this – always demanding more, wanting us to play better and trying to win the games earlier or in a different way," said Mata.
"We feel the manager is a great manager who has brought a strong mentality.
"This club is made for a winning mentality and I think he has it. He has had success in different countries.
"We are happy with him and the way he works. Everything is new but we are adapting well to his style of football."
Despite taking a 3-0 lead against Roma thanks to a goal from Mata and Wayne Rooney double, United were made to hold on for a 3-2 win after conceding twice late on.
Van Gaal vented his frustrations at his side’s inability to keep possession, saying that “it was not a good performance”, but Mata welcomed his honest approach.
"After the game, when we had given two goals away, he was not very happy but I think his way is that of a great manager," he said.
"He is very honest with the players, he says what he thinks and has a clear way of understanding football."