Sturridge was handed his first Champions League start for the club due to an eye injury suffered by Roberto Firmino at the weekend, and marked the occasion by opening the scoring during his side's eventual 3-2 win.
Firmino also came off the bench to score a stoppage-time winner in the Group C clash, and Klopp reserved special praise for both of his forwards after the match.
"It was really important we started like we did. We were so strong and good with the ball," Klopp told BT Sport.
"We changed the system because we expected a change from them. We needed all of our focus and we covered a lot of yards and closed all of the gaps.
"Daniel played a super game. I have never seen him as fit as he is in the moment. He was everywhere. He helped left and right and he was in the box when he was needed. Then you can bring Bobby Firmino on and that helps a lot. I loved his goal celebration."
Liverpool have now won their opening six matches of the season - their best run of form since 2014.