Sturridge's double helped his side to a 2-1 victory at Anfield on Tuesday as they reached the EFL Cup quarter-finals.
The goals were the England international's first for the club since August, but Klopp said there was never any question over the 27-year-old's talent.
"That's his talent, that's his strength. He's a finisher, he's a really good striker, there's no doubt about this," the German said.
"I was never in doubt about this, even when he didn't score. That's not in question. We don't have to discuss the quality.
"Divock Origi didn't score tonight but he played quite well. Danny Ings didn't score when he came in but he played really well.
"Daniel scored wonderful goals for us, really important. In the right moments, he and other players could have scored, and then it would have been perfect. It was really good."
Sturridge scored from close range in the ninth minute before finishing in a one-on-one with Michel Vorm just after the hour-mark.
Klopp also reserved praise for midfielder Kevin Stewart, saying: "He was good, very good. He is very important.
"I've said it a few times, he is the best challenger in the squad. An outstanding challenger – one-on-one situations, he is really ugly to play against.
"He is a good footballer as well. A good player and a good game."