The Irishman, 22, was picked instead of Adrian to replace Alisson, who was ruled out with a hamstring injury.
Kelleher pulled off a marvellous save to deny a late equaliser from Ajax, and Klopp was delighted with his performance.
Klopp said: "I think Adrian did an incredible job for us last season, clean sheets, Super Cup final.
"But now in this game we needed the natural football playing ability of Kelleher, so we made that decision. I am really happy with how calm and good Kelleher was."