Sturridge netted the second and was heavily involved in the other two goals of Liverpool's 3-0 win over Villarreal at Anfield on Thursday.
The win completed a 3-1 aggregate victory for Klopp's men, who moved into the decider against Sevilla.
Sturridge finally appears to have overcome his injury worries and Klopp said the England international was incredible at his best.
"[He played a] great game," he said. "You all see now when Daniel Sturridge is fit he is an unbelievable striker. But even he needs players to play with.
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"I know about his quality. I knew before I came here. Now I know it better. He's a good player and it is good to have him here."
Led by Sturridge, Liverpool moved into their second final of the season – having lost the League Cup decider to Manchester City.
Klopp said his side had shown their quality on their European run, leading to the club's first continental final since the 2007 Champions League.
"I think this year we have shown a lot of times what we are capable of and what they could be capable of in the future, so that is really nice and a really good sign," he said.
"That is more important for me as a manager, but when you perform in the right moments like we did tonight, against [Borussia] Dortmund or against [Manchester] United and Augsburg, then you want to have it all.
"Nine years between the last final and this one. Europe is big. A lot of teams want to go to finals. It is not too easy. Now we are there and it is a great opportunity and we will take it as that."