The Japanese star, who moved from German outfit Borussia Dortmund for a fee of €16 million (£13m) this summer, has impressed in the club's pre-season tour.
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He told reporters: "Every time I practise with my team mates is satisfying. When I get used to my new surroundings more I'll do even better.
"I know most of them know I could do better, and bring out their strong points.
"I feel as though I should be making more chances to get goals."
Kagawa has recently been praised by team-mate Rio Ferdinand and the playmaker hopes that his versatility will lead to extra first-team chances this term.
The Japanese icon added: "Having reliable players on both sides of me makes things easier.
"I can play in one or two positions, and if I play in one of them I'll get hold of the ball, I'll be able to create goals.
"I'll keep trying for good form so my team-mates can trust me and my presence in the team."