A meek title defence cost manager David Moyes his job last month and interim boss Ryan Giggs was left to guide the club into seventh place, leaving them without European football next season for the first time in 25 years.
Mata arrived at Old Trafford in January and has made 15 appearances in the Premier League, scoring six goals, but he was unable to revive their fortunes.
The Spaniard netted United's goal in their 1-1 draw with Southampton on the final day of the season and expects the club to come back stronger under their new manager, widely tipped to be Netherlands Louis van Gaal.
"Personally, I'm quite happy because I've played a lot of games, I've scored six goals and gave five assists, so I'm happy with my job," he told MUTV.
"But obviously I wanted to win more games, we lost games where we didn't play very well, so I'm not happy with that.
"I'll keep going to fight for the titles.
"I'm looking forward to next season to see how I can perform and how we can be back even stronger.
"The best (thing to do) is to come back and win trophies, so we will try to do that next season."
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