Despite picking up a league winners' medal as United secured their 20th title the Japan international was not satisfied from a personal point of view.
"It was a tough time for me with a lot going on in my head," said Kagawa of his first season after his move from Borussia Dortmund. "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."
He added: "Despite that, it was great we won the league, I just don't feel that I achieved everything that I wanted. For me personally, it wasn't a good season."
Kagawa arrived at Old Trafford last summer with an impressive reputation but United never really saw the sort of form he regularly displayed in Germany.
Having been brought in by Sir Alex Ferguson the 24-year-old now has to impress new manager David Moyes.
"I always think that I must play well," he told premierleague.com. "And I always have an image in my mind of how I want to play, wherever the position.
"Whenever there is a tough time, whenever it gets difficult for me, I just train and look ahead to the future."