Kagawa was excellent this season in United's 1-0 win over Real Sociedad on Wednesday night.
"I thought it was Shinji's best game in my time here," Moyes said.
"He hadn't really found his feet yet but I saw something from Shinji tonight which I hadn't seen in other games, so I was really pleased.
"His effort when we didn't have the ball was fantastic. With Shinji, everybody tells me about his ability and what he has got, but tonight is the first time I’ve really seen Shinji.
"I thought when we put him into the no.10 role, and even after it, he was good with Wayne. His attitude and energy were excellent and I was pleased for him."
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