The Japanese international caught the eye with a number of impressive performances for United after completing a summer switch from Bundesliga champions Borussia Dortmund.
However, a knee injury kept him out for several months at the end of 2012, and the 23-year-old admitted it was frustrating in his first season in England.
"I'm not satisfied so far, but then I am always very critical of my own performances. Even worse, though, I got injured," Kagawa told the club's official website.
"I had to go through the frustrations that come with getting injured in my first season with the team. Now I'm just doing my best to catch up on what I have missed.
"I'm confident my hard work will pay off."
The attacking midfielder has been played in numerous positions so far as Sir Alex Ferguson tries to discover where he is most effective, and Kagawa insists he is willing to play anywhere he is required.
"I have the most experience, from my time at Dortmund, in playing behind the striker," he added.
"However, I just want to be part of the team. I will play wherever the manager wants me to play."
He also went on to light-heartedly reveals that there are certain adjustments to life in Manchester he is still struggling with.
"The weather is not as good as I imagined! It rains a lot and it's often cloudy, but I am slowly getting used to it."