Salah, 25, joined Liverpool in a £38million move from Roma in June, arriving for a second stint in the Premier League.
Liverpool 8/1 to beat Leicester 1-0
Although his team have made a slow start to the campaign, the Egypt international has delivered with three goals and an assist in five league games, while he has also netted twice in the Champions League.
Klopp said landing Salah so early in the close-season was crucial to how well the former Chelsea attacker has settled.
“You should never take things like this for granted but I’m not surprised by how quickly he has adapted,” he said.
“He had a whole pre-season, so it is not as if he has had to settle in in a minute, which is what people are now expecting of Ox [Alex Oxlade-Chamberlain].
“He has been working with us for many weeks, so it’s no problem for him.”
Despite Salah’s fine start to life at Anfield, Liverpool have collected just eight points from their opening five games ahead of Saturday’s trip to Leicester City.
While Klopp was unwilling to label the signing a bargain, the German said Salah had impressed.
“What was it, £38m? I can never say a fee like this was cheap. But he’s a very good player, one we were convinced about. That’s why we did it,” he said.
“You could see in the first game at Watford, it was quite difficult. It was really physical and maybe a few people had doubts and thought it would be difficult for him.
“But he played better than anyone could have imagined. He was at Chelsea, but he was a kid there. Now he’s much more mature and everything is better.”
