Kagawa featured 26 times for the Reds in his debut season, scoring a total of six goals, but despite a promising start to his United career, Kagawa admits he is not happy with his performances.
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"The club has a long history and it was great that I could play in Sir Alex Ferguson's last season.
"At first there were also moments when I felt a bit lost but I tried not to give too much importance on such a feeling."
The 24-year-old has revealed his determination to improve ahead of the upcoming season and also next year's World Cup in Brazil.
"All I can do is keep showing what I can," Kagawa continued. "I have no excuse any more after a year in the Premier League.
"I know I'm at a place where you can't play if you don't achieve results. I'm determined to do it, also because there will be World Cup.
"It's really an important year for me."
The former Borussia Dortmund player also revealed his desire to win the Champions League after watching his former club in the final, and also suggested a return to the Bundesliga side in the future.
He added: "Watching Dortmund play in the final, I really thought I want to do well in that stage, in the Champions League."
When asked if he would return, Kagawa replied: "Yes, one day I will. If Dortmund are ok with it."