Salah took his tally to 50 goals for the Premier League club after netting a brace in a 4-0 Champions League win on Wednesday.
He became the fastest to 50 goals in Liverpool history, reaching that mark in just 65 games.
But the Egypt international's celebrations caught the eye on the night for how tame they were, with the forward having moved onto six goals in 13 games this season
Liverpool boss Klopp had no worries over his star man, however, playing down any thoughts that Salah was unhappy despite the goals scored. .
"He is completely fine," the German said in his post-match press conference. "Really. If he is not celebrating, I don't know if he is maybe a bit annoyed about getting asked about it [his scoring record].
"We didn't speak about it, to be honest. You ask him all the time and then I go to him and say, 'How do you feel because you haven't scored as often?' – I am not crazy! It is all good.
"I saw him celebrating but I couldn't see his face from that distance. I know he is fine – and I saw his face when I took him off. That was different."
Salah has scored in both games for Liverpool since the international break, having netted the only strike of the game at the weekend against Huddersfield, having not scored since a 3-0 win over Southampton in September prior to the break.