The reigning Premier League champions are currently lying in seventh position - a massive 11 points off Liverpool, who occupy fourth spot.
But Spain international Mata, who joined the Old Trafford club in a club-record £37.1m deal from Chelsea, insists David Moyes has a squad good enough to compete with the best.
"The objective is to get to the Champions League spots," Mata told Spanish TV station Canal Plus.
"It's difficult because Liverpool are doing well, so are Arsenal, as well as Tottenham and Everton, who are all clubs also fighting for them, but I think we have a team who can do it.
"This is Manchester United. When this club wins two, three or four matches in a row, it has a winner's mentality.
"We are coming and I think we can do it, but we have to win a lot of games first."
The 25-year-old, who has spent five days away with the rest of the squad for warm-weather training in Dubai, says Moyes has made him feel 'important' since joining the club in January.
"He made me feel important and I think that's fundamental when you arrive at such a big club that has made a huge investment in you," he said.
"It's nice when the manager tells you "Juan, you're important to the team and we need you on the ball as much as possible" and that's what I try to do.
"My relationship with him is good, friendly and from the off, he seemed to me to be a great person."
Mata is also confident the Scot will bring in world class players in the summer to help rejuvenate the club.
He added: "The manager said the other day at a press conference that he's going to be signing players.
"I think this club is at a stage of change, a bit of change in the project, but as I'll tell you, at this club the best players in the world will always arrive."