The Argentine has impressed at Old Trafford following his summer move from Real Madrid for a reported club-record £59.7m fee.
"The people here are amazing," Di Maria told the club's official website. "I feel really comfortable, very happy and really pleased. The way that people treat you really makes you feel good in your heart.
"When we are coming out after training or after the games, I have had a chance to meet some of the fans and it makes me happy that they love us so much and have got so much affection for us.
"I am trying to do my best to pay them back when I am on the field, so that the people are happy. They are really polite, they are always saying please and always saying thank you. That is really nice and I am really happy here."
Di Maria, who has scored two goals so far this season, is expected to play in this Sunday's derby against Manchester City at the Etihad Stadium.