Van Gaal has only been in his new job for six days, but his arrival has lifted the squad and Mata is looking forward to a successful season under the Dutchman.
United finished 22 points behind winners Manchester City under former manager David Moyes, but Mata sees no reason why his team cannot challenge for the Barclays Premier League and other trophies under Van Gaal.
United's club-record signing told MUTV: "It's the start of a new era for the club, with a new manager and players coming in.
"I'm really happy with the manager's style of football and hopefully at the end of the season we can celebrate something, which would be amazing for him and for us.
"We're focused on improving and trying to learn from the manager, to play at our best level during the season. The main idea is to play as a team and compete for titles."
Mata and his team-mates have been keen to impress Van Gaal during intense double-training sessions during the club's tour of America.
United fans will get a first glimpse of their new boss in the dugout on Wednesday night when the Red Devils take on the Los Angeles Galaxy at the Rose Bowl in Pasadena.
"The most important thing is to get ready, step by step, and not too hard because injuries can happen," the Spaniard added.
"It's important for us to prepare physically and mentally for the long season."
Van Gaal will speak for the first time on the tour on Tuesday at a press conference in the 92,542 capacity Rose Bowl stadium which will host the match.
Following the game against the Galaxy, United will head to Denver, where they play Roma in the International Champions Cup.
Further matches against Inter Milan in Washington and Real Madrid in Michigan follow, as well as a potential final against City, Liverpool, Olympiacos or AC Milan in Miami should United top their group.