The attacking midfielder was forced out of the Blue Samurai's World Cup qualifier with Iraq last week before sitting on the bench for the Red Devils' 4-0 home win over Wigan Athletic last Saturday.
On Wednesday night, Kagawa played 84 minutes of United's 1-0 Champions League victory over Turkish club Galatasaray, in which he supplied Michael Carrick's winner, and feels it was important to get back to form for his club.
But the ex-Borussia Dortmund star is of the belief that he can still improve once he fully increases his momentum.
"We got off to a good start at home," Kagawa told Nikkanafter the match. "We had two or three chances to score, and then when we did convert it became an easier game to play.
"Nothing's hurting," he said in regard to the injury. "I've gotten back into form in practice, but I need to improve a bit more physically and increase my momentum."