The Spaniard says that the Scot, who was sacked on Tuesday, played a crucial role in his move from Chelsea to Old Trafford, while dedicating Saturday's win to the club's fans
Mata joined the 2012-13 Premier League champions in January for a club-record fee of £37.1 million after Chelsea manager Jose Mourinho deemed the Spaniard surplus to requirements at Stamford Bridge.
And although United have struggled this campaign, the attacking midfielder has slotted in admirably, scoring twice from the bench in Ryan Giggs's first game as interim manager against Norwich City on Saturday.
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"I wish him and his technical staff the best of luck in the future and I do thank him for his continuous interest in me and his importance during my transfer to become a Manchester United player.
"The season goes on, although just for three more games, which makes me kind of sad because I'm feeling really good and I would love this Premier League to last a few more weeks."
United put struggling Norwich to the sword at Old Trafford on Saturday, with Wayne Rooney grabbing the opening two goals before Mata tapped home another two in the second period of a 4-0 win.
And the Spaniard feels that a victory of this size was not only important in Giggs's first game in charge but also as a way to repay the supporters after a below-par year.
"It was Ryan Giggs's first game as a manager after plenty of years of success on the pitch and the truth is everything went well," Mata enthused.
"Our fans deserve that, indeed. They deserve scores like this one because, in this tough season, they have gone home with a downcast face too many times so that's what we are going to try in the remaining games.
"That win was extremely important for sure, since it was a happy ending to a complicated week with big changes."