Park has left United for QPR just as Kagawa begins his Old Trafford career.
"This is only the beginning for me," Kagawa told the Mirror.
"But Park Ji-Sung is the best player Asia has ever produced - there's no doubt about that.
"He played regularly for United for a long time and I can't be sure how long it will take me to establish myself in the team like him. But I will always work hard to do so.
"Watching him play for United motivated me a lot. I began to truly believe Asian players could play in big clubs.
"I was expecting we could help each other and play together at United. It's a shame that he left.
"But, like Park, I will focus every day on training and do my best to stay here a long time."