The Spain international arrived at Old Trafford in a £37.1million deal from Premier League rivals Chelsea in January and has had an immediate impact, assisting goals in three of his first four league outings for the Red Devils.
Having failed to win their last three matches, though, David Moyes' men are now 11 points adrift of Liverpool, who currently occupy fourth spot, but Mata has refused to concede defeat in the race for Champions League football.
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"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."
Mata moved to Old Trafford after falling out of favour with Chelsea boss Jose Mourinho, and the 25-year-old says he is made to feel valued by new manager David Moyes.
"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," the former Valencia man added.
"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."