The former Borussia Dortmund midfielder made only his second start of the season in Wednesday's League Cup tie against Liverpool, which United won 1-0 through a 46th-minute goal from Javier Hernandez.
Initially deployed wide on the left, the 24-year-old became more influential as the game wore on, grazing the crossbar with a 25-yard drive in the second half before being withdrawn in the 73rd minute.
After a mixed first season at Old Trafford, Kagawa is yet to prove his true worth in United's colours, but Moyes said he was still working his way towards full fitness.
"He did OK. I thought he grew into the game a little bit more," Moyes told reporters after Wednesday's game.
"There were bits which I was pleased with, and bits where we were looking for a little bit more. Overall, he's still getting back.
"A lot's been said (about his lack of playing time), but I think most people who watched would say he's still short of being really at full match fitness."