The Spaniard, who became the club's record signing when he joined for £37.1m from Chelsea over the weekend, made his debut on Tuesday night and played all but the last seven minutes of the 2-0 victory over Cardiff.
And the 25-year-old thinks United, currently in seventh, are poised to start climbing the table over the remainder of the season.
"I have felt comfortable at this club from the first minute," said Mata. "Time has gone so quickly but the welcome has been amazing.
"The lads are really good and there is a great atmosphere.
"I am always positive. If any club can come back and climb the table, it is this one.
"It will take time but hopefully we can go back up the table. That is what we have been talking about in the dressing room.
"We will try to win as many games as we can to the end of the season, hopefully all of them."
More to come from Mata
Mata produced a polished display on his debut but says there is more to come, adding: "To be honest I didn't train that much last week because of the transfer. I know I can improve."
Robin Van Persie and Wayne Rooney both featured against Cardiff after recovering from injuries and Mata is looking forward to teaming up with them in the coming months.
"Rooney and Robin are two of the best strikers in the world," said Mata.
"It will be amazing to play alongside them. I just want to help them, and help the team win matches.
"We need to sustain this feeling."
Strong bench pleases Moyes
United boss David Moyes is also in upbeat mood, pointing to the fact that Rooney and exciting youngster Adnan Januzaj started on the bench as evidence that United now have the strength in depth they need.
"People would have looked at our bench and said 'that is more like it'," said the manager. "We are starting to get players in.
"I need competition and I need players to play well, we have not had enough right at the top of their game. Hopefully, the competition for places will help make that happen."