Kagawa, who signed for United from Borussia Dortmund this summer for £14m, was influential in the midfield yesterday and capped his performance with a goal.
"I worried that I might have been offside," Kagawa told Nikkan. "I'm glad the timing worked out. I wanted to score a goal somehow, so I'm relieved I could do so at our first home game.
"It's important that I keep playing well in each match. I don't have time to enjoy the moment. Next time I want to score a goal on my own terms."
Kagawa also hit the post with a shot from the edge of the box in yesterday's game.