The Samurai Blue lost 2-0 to Serbia and 1-0 to Belarus in their two friendlies over the international break and the former Borussia Dortmund man believes the "tough times" he is enduring with the Premier League champions have affected his fitness and mentality.
After reporting back for pre-season later than most due to his Confederations Cup exploits, the 24-year-old has featured in only four of the Red Devils' 11 games so far this season.
"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," Kagawa told reporters in Japan.
"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," he explained when asked how his lack of club action was a problem, "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."