Kagawa was handed a start for the 1-0 triumph.
"I thought it looked like his first game back for a while," Moyes said. "He had a bit of illness and just hadn't looked right in training.
"I thought Norwich might be the right opportunity, but I still thought he looked as if he was blowing. But he will get better.
"He's a bit like that. I think when he plays he gets better. After about 60-65 minutes I thought it was time to come off."