The Brazil international briefly became the most expensive goalkeeper in world football when completing a £65 million ($81m) transfer over the summer.
He has been spared the pressure of that standing by Kepa Arrizabalga’s £71m ($89m) switch to Chelsea and is thriving in new surroundings at Anfield.
Alisson has conceded fewer goals than any of his Premier League rivals, while he has also helped to carry Liverpool into the last 16 of Europe’s elite club competition .
He was called upon in the closing stage of a must-win meeting with Napoli on Tuesday, and stood tall in stoppage-time to make a vital stop from Arek Milik and seal a 1-0 victory.
Klopp told Viasport afterwards: “The goalie made the save of the season.
“I have no clue how he made that save ... Thank God we have him.
“If I'd known how good he was, I’d have paid double.
“I think nobody expected a save in that situation. It’s a goal, no?"
Alisson managed to block the ball away from Milik after the Napoli striker had drifted beyond the Liverpool defence and found space just six yards from goal.
Klopp concedes that he was living on his nerves by the time his No. 1 repaid a large chunk of a sizeable fee, with the Reds’ fate left hanging in the balance until the very last kick.
The German said: “After 65 minutes, it was really wild. Counter, counter, counter.
“The save Alisson made I have no words. It was life-saving tonight.
“It wasn’t just one save - he had a lot of things to do and did it so coolly and calmly. Still he did it, incredible, unbelievable, never saw anything like it.”
Alisson’s heroics mean that Liverpool will be back for more Champions League action in the new year, having made their final all the way to the final last season.
They will discover their opponents for the next stage on December 17, and Klopp claims to have no preference when it comes to the next challenge put in front of him.
He added: “Until 7.55 tonight I wasn’t sure we would even be in the draw. I don’t care who we draw.”
Of more pressing concern for Liverpool is a Premier League meeting with old adversaries Manchester United on Sunday.