Kagawa, who was signed by Sir Alex Ferguson last summer, has played just seven minutes for Moyes's United this term, coming off the bench in the Community Shield win over Wigan in August.
But, after scoring a fine goal for Japan in Tuesday's 3-1 win over Ghana, the playmaker took the chance to concede he was disappointed by a peripheral role at Old Trafford.
"Please ask David Moyes why I'm not in the side," Kagawa, left out of the United squad beaten by Liverpool before the international break, told the AFP news agency.
"It is frustrating not playing but to score a goal like that gives me confidence. Hopefully I can take that back to my club with me and things will improve.
"It's hard not playing regularly. Some days the frustration is worse than others; it comes in waves.
"So it's nice to come back to Japan and get to play, and to score felt good.
"I just have to keep working hard and keep pushing for my chance. When I get back it will be a challenge to get into the team.
"When I get back to my club I have to wait for my chance in the Champions League and the Premier League. I'm sure my chance will come."