The Japan international is still bedding in after arriving from Borussia Dortmund last summer and, although a knee injury stunted his early promise, it was telling the manager entrusted him with a key role during Wednesday's 1-1 draw with Real Madrid.
Many see Kagawa as an important figure in European competition for the Reds and the boss acknowledges he provided a threat early on at the Bernabeu.
"In the first half an hour [in midweek] he was terrific as he kept making these great runs through them, which we thought was going to be one of our biggest assets in the game," Sir Alex explained.
"He was just unlucky that he had a couple of heavy touches on the ball when he made runs past Robin van Persie. He kept opening them up but people don't see that, which is a wee bit unfair, as he did really well for us in the first half."
Sir Alex is convinced the 23-year-old will only begin to show his true colours after having a full season to settle at Old Trafford.
"He's come from an environment that is completely different," he stated. "I think the difference between German football and English football has been shown. In Germany you can't foul. It's foul after foul.
"The Premier League is completely different as there's physical contact in our game and it's different to Germany but, next year, he'll be better."