The £13million signing from Stoke City scored with a breathtaking bicycle kick in the Reds' 4-1 thumping of United in Michigan.
"That's not normal after four days in the club - adapting that well to the style of play," Klopp said.
“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.
“It was better than I would have expected, to be honest. I think today it was a game where it was quite easy to come in for pretty much all of them because we played over 90 minutes of really good football on a very difficult pitch for both teams.
“We still played simple and quick, kept them moving. After the Dortmund game, I didn't feel really good but I knew I don't have to make it bigger than it is.
“It's a pre-season game so if you make mistakes you should lose - if you learn from it that's okay. Today we don't make it bigger of course
“For Shaq, in 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, 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."