The former Borussia Dortmund playmaker has found game time limited at Old Trafford, making just one Premier League start for David Moyes' men this season.
And Kagawa admits to have felt the adverse effects as his country fell to 2-0 and 1-0 losses against Serbia and Belarus, respectively.
"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," he said.
"During tough times like these I have to improve myself.
"Personally, I felt strongly after these two matches that I need to play more (at my club) and, as a team, there are many things we need to do as well.
"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."
Japan qualified for the FIFA World Cup in June, topping Group B in the final round of AFC qualifying.
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