The 23-year-old, substituted after an hour last Sunday in United's 1-1 draw at Tottenham, concedes he has found it tough going in England and knows he must improve on his current form.
"I'm really feeling that I need to perform better," said Kagawa. "I'm not satisfied with what I have done here at all.
"It's a big and really famous club in the world and I need to overcome lots of pressures and be mentally stronger.
"Unfortunately I got injured, but I have to be better and grow as a player a person, in terms of contributing to team's wins and succeeding here."