The Japan international arrived from Borussia Dortmund for £17million last summer and was immediately in awe of Ferguson's stature at the club.
"He has a magnetic power," Kagawa told the club's official website.
"I felt it the first time I met him, from the way he conducts himself and also from working with him on the pitch.
"He communicates well with his players and respects them. As the season went on, I got to communicate with him more, both on football and other subjects. That was important.
"He is a friendly person and his spirit is much younger than his age. I think that's because of his achievements over the years, and also his personality.
"I wish I could have played much longer under him. What he has achieved for the club is tremendous - he is in a class of his own."
Although Kagawa has had a mixed year under Ferguson this term, the 24 year-old regretted the chance of not being able to play more for the Scot.
"I wish I could have played much longer under him. What he has achieved for the club is tremendous - he is in a class of his own," he added.