The Japanese star scored his first goal since moving from Borussia Dortmund and it was enough to win the Chevrolet China Cup following a 1-0 victory. Kagawa fired home a pull-back by Bebe as United dominated the match in humid conditions.
"I was very pleased," said the boss. "In the second half, we did well and upped the tempo of the game and tried to get more players into the penalty box.
"We were a bit pedantic in the first half but it's been a great work-out. They had to really run a lot because Shanghai were very well organised, as you saw, with 11 men behind the ball all the time. It's not easy to play against but we could've scored a few goals.
"I think we had plenty of possession of the ball and Kagawa was involved in most of that. He was man of the match and he deserved that. He took his goal quite well, although it was a deflection. It was good work by Bebe too, who set it up for him. I think Bebe did really well when he came on.
"Kagawa has settled in well. He's going to be a really good player and he impressed tonight. His awareness of receiving the ball, his speed in turning and how he attacks defenders is an asset to us."
Sir Alex was talking to MUTV and at a press conference.