The Japan playmaker brilliantly set up the first for Ciro Immobile, and had a hand in one of Adrian Ramos' two goals as Dortmund went three points clear at the Group D summit in the UEFA Champions League.
"I thought Kagawa did very well," said Klopp. "He played some great passes.
"He produced a big performance. He was very important for us, without doubt."
Klopp was also impressed with Sebastian Kehl's display, but was concerned the midfielder picked up a knock on his return from injury.
"Kehl had a very good game, but I only want to continue talking about him when I know that he can play in the next game," said the Dortmund coach.
"I am a very superstitious man. He got a blow on the foot, so I will wait and see."
Kehl himself was relieved Dortmund responded in style to pocketing just one point from their last three Bundesliga games.
"The team wanted to show a reaction, you could really feel that," he said. "We started very well and took one of our early chances. It was a great team effort."
