Kagawa made his debut in the victory over AmaZulu.
"My team-mates all welcomed me very warmly and I'm enjoying every single day here," he told MUTV.
"This is a great club and I'm looking forward to playing. I have to prove myself on the pitch.
"I've joined the club but I've not shown my potential yet, so this is my first mission and I hope I can show all the supporters what I am able to do."