The Serbian midfielder reunited with manager Jose Mourinho at Old Trafford after joining from Chelsea earlier this summer in a reported £40m deal.
After the game, Matic told MUTV: "Thanks to the guys, they have accepted me from my first day and I feel their support. Thanks to them, I feel very comfortable and I feel like I will be here a long time.
"They have helped me, and I am happy if I give them something back, and that I helped us to win. We played good football, and I think our supporters enjoyed it as well. It's good to start well with three points, the season is long but we have to collect a lot of points and we've had a good start.
"It was great [to play at Old Trafford], when you wear that shirt you feel some kind of pressure because this is a big club, but that's why we are here. We know that it's a big responsibility to play for Manchester United and I'm happy that we have started well and that I hope we continue like this - I'm sure this group can do good things."
United's next league game is away against Swansea City this Saturday.