The summer signing, who has struggled with injuries this term, opened the scoring just before half-time before coolly adding his second and third in the latter stages of the contest as he became the first Asian player to score a Premier League treble.
And Sir Alex was keen to cite persistent setbacks as the reason behind Kagawa’s slow start at the club, before promising the fans that the best is yet to come from the Japan international.
"It was a brilliant day for him, he is a good finisher. His second goal was composed and intelligent, his last was brilliant," he told reporters.
"He missed that period of football in October and November that set him back a bit. He is gradually getting his form back but next year he will be far better, you will see a really good player then."
The 71-year-old boss also spoke of the imminent Champions League encounter with Real Madrid and predicted that both teams would score in what would be a "fantastic night".
"It will be a fantastic night, you are talking about two of the greatest clubs in the world. Emotions will be high and I am sure it will be a tremendous match," he continued.
"If we can get a blank against us on Tuesday we would go through. But I think both teams will score. I just hope we get more than them."