Kagawa has made a positive impression at Old Trafford after making the move from Borussia Dortmund in the summer, scoring twice from seven starts.
Sir Alex Ferguson has been happy with how Kagawa is settling into his new surroundings, saying: "We're very pleased with Shinji. Adapting to English football isn't easy but bit by bit he's getting down to that part."
Ferguson has nevertheless made it clear that he is working hard to try and help Kagawa improve, and the Japan international has revealed one of the messages he has received.
"Don't face the goal with your back, but move your body so you have a short way to the goal. Shape your body so you are facing the stands," Kagawa said. "I have to face the goal or I won't be a threat."
The 23-year-old also recognises that he has to do more to cope with the physical rigours of English football, saying in The Independent: "I've realised that I need to limber up and strengthen my body trunk."
Kagawa has also learnt a lot from how Manchester United beat Galatasaray in the UEFA Champions League despite an unconvincing performance.
He explained: "Dortmund would have lost that match. I think that winning a game (that) way is characteristic of a big club.
"The level of expectation is very high and that means that the team is not in a hurry to win. That's the main difference with Dortmund."