The Spain international arrived at Old Trafford in a £37.1 million deal from Premier League rivals Chelsea in January.
Mata's arrival had an immediate impact as United beat Cardiff City 2-0 on his debut, but a 2-1 defeat at Stoke has been followed by draws with Fulham and Arsenal.
That leaves the reigning champions some 11 points adrift of Liverpool, who currently occupy fourth spot, but Mata has refused to concede defeat in the race for Champions League football.
"The objective is to get to the Champions League spots," he told 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."
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."
