Mata completed a £37.1 million move from Chelsea to Old Trafford on Saturday and was unveiled by the reigning league champions on Monday.
Arsenal are currently 14 points ahead of United, but the Spain international thinks his new club has the character to take top spot.
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"To be honest, what I like most about Manchester United is the character," he told reporters. "I think for other clubs to be in this position down in the league it would be very, very difficult for that club to come back and take first position. I think this club can do it.
"This club is used to fighting until the end, to get the results they want, to show character, this is the real image I have of Man United, to fight for wins, to fight for titles, to come back always from difficult moments."
The former Valencia man also commented on his former club Chelsea, describing his final six months at Stamford Bridge as difficult.
He continued: "The last six months I didn't play as much as I wanted to but I respect Jose Mourinho, he is a top manager, I respect my team-mates.
"I tried my best in every game, every training, but when Man Utd came in it was a great option for me to carry on my career."