Kagawa struck his first goal for United in victory over Fulham on Saturday.
He told the Daily Mail: "The physical side of it is the first thing. I need to adapt to that. The other thing is the quality through the division. In Germany, the top few teams were so much better than the rest, but, here, every opponent is difficult.
"We seem to pass the ball sideways a lot, but I want team-mates to start giving me the ball from all areas and angles. I need to speak to them about this, because I want them to have the trust in me to play the ball forward."