The young Irishman enjoyed a fine European bow, making several smart reaction saves and keeping a cleansheet as the Anfield side secured top spot in Group _ thanks to a goal from Curtis Jones.
Previously, Kelleher had been seen as the third option in the goalkeeping rotation at Liverpool, with Adrian ahead of him.
The Spanish goalkeeper, however, has made a series of high-profile errors in the past, and while Klopp was careful not to criticise the former West Ham man, he was equally effusive with his praise of the 22-year-old.
“Top, top. Top,” he replied when asked to comment on Kelleher’s performance
“It was easy to decide for Caoimh because he deserved it but Adrian has done really well too. He’s kept lots of clean sheets before, in the European Super Cup last year, but tonight we needed Caoimh's package.
“He’s a top footballer and we needed that because of Ajax's pressing.”
Asked how the youngster was handling the buzz of the match, he replied: “I am pretty sure he will either sleep really well or not all! Hopefully he will enjoy both.”
Ajax were very competitive for long periods of the match, but that did not surprise Klopp, who had to name a much-changed side because of injury problems.
“I’m not surprised it was an open game,” he said. “I'm over the moon with the attitude and character. It’s not the moment of the year to play the best football.
“We defended well which is a big part, had counter-attacking chances and had to defend with all we have. Ajax were in the game.
“I am very, very happy with the result and performance in the circumstances. Great.”
Liverpool have already won their group and will therefore have the luxury of rotation when they face Danish champions Midtjylland next week – a match in which neither side has anything on the line.