United have vitually guaranteed their place in next season's Champions League following their 2-1 victory over Crystal Palace on Saturday.
But, United now have a chance of breaking into the top three and earning automatic entry into the Champions League group stages after Arsenal suffered a shock 1-0 defeat to Swansea on Monday.
"We are virtually qualified for the next Champions League, which is the least this club must achieve," Mata wrote on his blog. "It's true that being fourth we would have to play a qualifying round, but we will try to finish even higher, although in order to do so we don't depend just on ourselves. But it was vital for us to secure, at least, the fourth spot."
United could jump ahead of Arsenal into third place on the points table if they manage to beat the Gunners on Sunday.
With Arsenal coming off a painful loss to Swansea, Mata believes that United can use their positive momentum and the Gunners' disappointing performance to walk away with a win at Old Trafford.
"The Palace win was a boost of confidence for us ahead of our game against Arsenal next Sunday, the last game at Old Trafford this season and regardless of the table, it's a game we have to win," he wrote. "We owe that to our fans: they have always been supportive throughout the season, when we played good and when we didn't.
"We want to have a good farewell in Old Trafford for them, though there is also one more game – away against Hull — that we will try to win as well."
Mata also took the opportunity to personally welcome Memphis Depay, who has signed with United from PSV Eindhoven.
"We know about the signing of Memphis Depay for the next season," he wrote. "He's a young footballer who has shown his quality in the Dutch League.
"Like any new teammate arriving here, he will be welcomed and we will help him to settle in quickly. But right now we must focus on the last two games."