The Red Devils are expected to challenge for the title after splashing around £150m on Victor Lindelof, Romelu Lukaku and Nemanja Matic.
Jose Mourinho's side kicked off their campaign with an impressive 4-0 win against West Ham at Old Trafford.
And Mata said: "It was a joy to have a game like this one, we needed it after failing to win the first title of the season in Skopje.
"I was really pleased to see our fans happy after the game, on their way home, and also your reactions on the social media, of course.
"I hope we can have many more games like that, even better if they are 37 :-).
"Obviously we know it will be complicated, because this is the toughest league in the world and every single game is a difficult test.
"These are the first three points, and they will be even more important at the end of the season."
United - criticised for their style of play in recent seasons - put on a scintillating display with Lukaku and Matic impressing on their debuts.
And Mata said on his blog: "The team worked harmoniously, we had some spells of great football and our shots on goal were good.
"Personally, I enjoyed myself on the pitch and I believe all my team-mates did the same.
"Some of them (Nemanja and Romelu) made their debut as Reds in the Theatre of Dreams and I’m sure they will always keep very nice memories of this day."
