The Egyptian winger is the Reds' top scorer so far this term with five goals in eight appearances since his club record move from Roma for an initial fee of £36.9million.
“Mo has played better than anyone could have imagined," Klopp said.
“He's a very good player, one we were convinced about. That's why we did it. You could see in the first game at Watford, it was quite difficult for him at the beginning. It was really physical and maybe a few people had doubts and thought it would be difficult for him.
“But now he's much more stable. When he was at Chelsea, he was only a kid there. Now he's much more mature - his style of play and also physically - everything is better.
“I'm not surprised but you should not take things like this for granted as sometimes new players need time."
The German continued: “He had a whole pre-season which changed everything so it's not settling in in a minute, which people now probably expect from Ox (Alex Oxlade-Chamberlain).
“Mo had a pre-season, good sessions, bad sessions, good games, less good games, so it's all good."
Considering how fees escalated this summer, the money Liverpool shelled out for Salah looks increasingly like a shrewd investment.
“What was it, £38 million? I can never say a fee like this was cheap or whatever," Klopp said. “But he has done well and hopefully he can stay like this."