Salah scored the fastest-ever hat-trick in Champions League history in the 7-1 win, coming within six minutes and 12 seconds.
The Egyptian had been brought on by Klopp in the 68th minute for Darwin Nunez before making his remarkable impact.
“Special. Typical Mo. Very important, the whole thing,” Klopp told reporters.
Rangers had gone ahead via Scott Arfield in the 17th minute before Roberto Firmino’s double earned the visitors the lead.
The Brazilian set up Nunez to make it 3-1, before Salah took over with all three of his goals assisted by substitute Diogo Jota.
Harvey Elliott grabbed a goal in the 87th minute after VAR intervention too.
“How the boys adapted to it, to the positions, to the line-up, the reaction of the boys on the pitch,” he said.
“I thought everybody who started tonight played really well. I cannot think of one player who didnt have a good game; the two kids of the right and left wing, really good, Fabio (Carvalho) and Harvey.
“And then when you can change like we changed tonight, if you can do that, the boys come on and are ready to contribute and things like this can happen.
“It’s a freak result and we all know that and we dont make more of it than we should, but obviously it is the best we could have asked for and that is why I am pretty pleased.”
Liverpool next face English champions Manchester City in the Premier League on Sunday.
“(The win) changed the mood, definitely,” the German said. “It is completely different. We usually drink a beer after away games, but it is that long ago that I drank beer and I probably will be drunk after one.
“We don’t have to make a big thing of it, but the best football team in the world right now is coming to Anfield on Sunday.
“We will see what we can do, but its not now that we are with a big mouth and telling them come and we are waiting. Not at all. It was for us tonight, for different reasons, incredibly important. Yes, 7-1 is a freak result, we know that.”