The Japanese international signed for United this summer from German champions Borussia Dortmund, where he sparkled in an advanced central position.
Kagawa thinks that if given time and patience he will come good and start to repay the faith of Sir Alex Ferguson.
He told Kyodo News: "To be honest, I don't believe I have yet cemented my place. I still feel I need more time to adapt.
"There is not one game that I can be satisfied with the way I played over the 90 minutes.
"I need to communicate better so I can get my timing right when asking for the ball and things like that. You gain trust when you deliver results."
The 23-year-old has scored two Premier League goals so far this season in six domestic appearances.