Kagawa was back in action for Japan this week.
"Personally, I felt strongly after these two matches that I need to play more and, as a team, there are many things we need to do," he said.
"So we all need to go back to our European or J-League clubs and take what we learned in these two matches and work to fix those problems.
"There's a matter of fitness and there's also that atmosphere of playing for my country. It's different from the atmosphere at United, but you still get a good feel for being on the pitch when you play regularly.
"Maybe it's because I'm not used to being on the pitch of late, but I didn't feel like I was able to enter these two games properly. During tough times like these I have to improve myself."
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