The 23-year-old scored the only goal of the match as Japan recorded a famous win in Paris, but the playmaker has refused to get carried away with the victory.
"It's an important result. Right now I'm in a tight spot with the team so I wanted to find some confidence," he told reporters.
"As a team we still have to improve, and it was a friendly so [Franck] Ribery didn't start, so if you think about it calmly there isn't quite a sense of having achieved anything."
Kagawa has scored two goals in six matches for United this season.