The Spain international arrived from Chelsea for a club record fee of around £37.5 million in January, but largely struggled to justify the fee as United lurched from one disaster to another under David Moyes.
Mata made 15 appearances for United and claimed six goals and four assists, but the creative playmaker was regularly played in a wide left position under Moyes, rather than his favoured role behind the striker.
The Scot was eventually sacked in April, and Van Gaal will take charge in the new season after his official unveiling last week.
Mata revealed that he enjoys Van Gaal's approach to working and thinks that the side can put aside last season's disastrous campaign to seriously challenge for silverware this season.
He told the club's official TV station: "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.
"The most important thing is to get ready, step by step, and not too hard because injuries can happen. It's important for us to prepare physically and mentally for the long season."
Mata also talked up the intensity of the club's pre-season preparations, but accepts that the hard work is necessary ahead of an arduous campaign.
"The running. You usually do two or three sessions a day, two outside and one in the gym," he added. "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."
United have already spent around £60million on Luke Shaw and Ander Herrera this summer, but much will also be expected of Mata following his big-money move earlier this year.
Van Gaal takes charge of his first game in the early hours of Thursday morning when the Red Devils take on LA Galaxy, and the Dutchman is understood to be keen to add to his squad further ahead of the new Premier League season.
Reports emerged on Monday claiming that United were planning an improved bid for Juventus midfielder Arturo Vidal, while Patrice Evra has now completed his move in the opposite direction.