The 24-year-old Japan international arrived at Old Trafford last summer from Borussia Dortmund with a big reputation and went on to collect a title winners' medal.
However, despite featuring regularly and scoring a fine hat-trick in the 4-0 victory over Norwich, Kagawa feels he can play much better.
"It was a tough time for me, with a lot going on in my head," he said.
"I am not happy with my performance for the team at all. I didn't score that much and I also had my (knee) injury.
"Despite that, it was great we won the league, but I just don't feel that I achieved everything that I wanted.
"For me personally, it wasn't a good season."
David Moyes has now taken over in charge at Old Trafford after Sir Alex Ferguson retired and Kagawa is hopeful of impressing the new man.
"Whenever there is a tough time, whenever it gets difficult for me, I just train and look ahead to the future," he told premierleague.com.
"I always think that I must play well and I always have an image in my mind of how I want to play, wherever the position."