Klopp was especially impressed with how the Switzerland attacker has hit the ground running for his new club, having only linked up with his teammates on Wednesday after his post-World Cup break.
"That's not normal after four days in the club - adapting that well to the style of play," the German is quoted by Goal.com as saying.
"We wanted to help him a little bit with the position [so] that it's not too complicated, gave him a lot of freedom, offensively playing natural, plus offering runs in behind, which is what he did especially around the Sturridge goal.
"For Shaq, the moment he signed, he wanted to stay immediately at Liverpool and train with us. I think it was a week after he finished the World Cup, so I said: 'No, no, no. Go'.
"He came back a few days ago and he was really excited. For him it was very good moment in his career, having already had a real experience at Bayern [Munich], at Stoke, at Inter. Those were important moments in his career and now we have him and he can now play together with a few really nice football players."