When Mata signed for United last January, the club were in the midst of a dreadful run of form that cost manager David Moyes his job.
Despite the £37.5million arrival of the Spaniard, United could only finish seventh and Moyes was replaced by Van Gaal.
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.
Van Gaal has only been in his position for six days, but his arrival has injected optimism into a squad previously short on confidence and Mata is looking forward to a successful season ahead.
United finished 22 points behind winners Manchester City last term, but Mata sees no reason why his team cannot challenge for the Barclays Premier League and other trophies under the vastly experienced Van Gaal.
"It's the start of a new era for the club, with a new manager and players coming in," United's club-record signing said.
"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 under the LA sun.
And if they needed another reminder that they are playing for their futures, then it was duly delivered by Ed Woodward on Sunday when he told United fans to expect more incomings and outgoings over the next few weeks.
While Mata understands the need for tough training, the Spaniard thinks it is important the players do not overdo it.
"The most important thing is to get ready, step by step, and not too hard because injuries can happen," the former Chelsea player told MUTV.
"It's important for us to prepare physically and mentally for the long season."
Like Mata, Chris Smalling will take part in the entire pre-season tour as England were knocked out of the World Cup at the group stages.
The centre-back is under pressure to establish himself as a first-team regular following the departures of Rio Ferdinand and Nemanja Vidic.
Smalling hopes the hard graft he and his team-mates are putting in during their stay in the US will be worthwhile.
When asked what the toughest part of pre-season is, the former Fulham defender said: "The running
You usually do two or three sessions a day, two outside and one in the gym.
"It's quite hard on your lungs and your legs, but you know that come August you'll be ready to last the distance for the 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.
Striker Javier Hernandez will join up with the squad on the eve of the match but is unlikely to play.
After 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 versus 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.
Source : PA
Source: PA