The 23-year-old midfielder made the move to Manchester after shining for Borussia Dortmund in the Bundesliga, but has been unhappy with his form since the transfer.
"I’m not satisfied so far, but then I am always very critical of my own performances," Kagawa told the club's official website. "Even worse, though, I got injured. I had to go through the frustrations that come with getting injured in my first season with the team."
The Japanese playmaker believes he faces a difficult task as he tries to catch up with the rest of the squad following a spate of injuries but insists he is working as hard as possible to do so.
"Now I’m just doing my best to catch up on what I have missed," Kagawa added. "There’s a lot of pressure when you play for this club, but all I can do at the moment is keep working hard every day to bring out the best in me. I’m confident my hard work will pay off."
Meanwhile, Kagawa is convinced that the season can only be considered a success if United manages to win the Premier League.
"A big club is expected to win every game and also to be the champions," Kagawa said. "So that’s definitely our goal. I’ll do my best to contribute to the team so that, come the end of the season, I can feel I’ve made a contribution to what will hopefully be a title win."