The Japanese international rejoined BVB at the end of August for just half of what United signed him for two years ago and has already settled back into life at the Westfalenstadion with a goal against Freiburg on Saturday.
"His first season at United was the last one of Sir Alex Ferguson, so that isn't the time to develop players," Klopp said.
"At that stage you only want results and titles.
"His second year was the first of the new coach, Moyes, so that was also all about results. Then there was a third manager, Van Gaal, with a very successful philosophy.
"We saw the chance to sign Kagawa and took it. He was sensational against Freiburg."
For the big stories and the banter follow us on Twitter: @tribalfootball