Kagawa, who arrived at Old Trafford from Borussia Dortmund last summer, started his debut season at United brightly but suffered a knee injury in October which kept him sidelined for two months.
The 24-year-old scored five goals in 18 Premier League outings for the club, including his hat-trick in the 4-0 success over Norwich last month.
The Japan international has earned plaudits in his home country after helping United to a 20th league title but believes he could have offered more to Sir Alex Ferguson's side.
He said: "I was looking to produce even more results. I was injured and I felt things didn't go well easily.
"I had a lot of conflict, frustration and worries. In that sense, I think it has been a profound year.
"Honestly, I haven't contributed as much as I did at Dortmund.
"I was even injured. I still don't quite have that feeling of accomplishment."
Despite feeling he could have offered more on an individual level, Kagawa was pleased to be part of three successive title wins after helping Dortmund to back-to-back championships following his move from J-League club Cerezo Osaka in 2010.
The midfielder is hoping to build on that tally, adding: "I've managed to win three in a row. I think my career is bound to get better and better."