The Japan international moved to Old Trafford from Borussia Dortmund last summer, and scored six goals as the Red Devils went on to win their 20th Premier League title.
However, having won back-to-back Bundesliga crowns and scoring 29 goals in two years with Dortmund, Kagawa believes that he could have made a greater contribution to United's campaign.
"It was great to win the title with United and to make it three in a row for me personally," Kagawa told Inside United. "But I feel I still have work to do. I would say I am half satisfied and half unsatisfied.
"I want to be a better player year by year. I expect a lot of myself. I hope to show my dynamism, style and presence more.
"I think it is very important to keep working in your everyday training and in matches. You just have to keep practising. But you must also have a strong will. That is the key to playing in a foreign country, especially for me in Europe."
Kagawa cost United around £17m.