Jones was the only player retained from Saturday's 3-1 win over West Ham, but dropped back from midfield to fill in on the right side of defence in the absence of Trent Alexander-Arnold and Joe Gomez, with Stefan Bajcetic on the bench after playing right-back against LASK last week.
Even with plenty of experience in the side, the 22-year-old Jones took the armband as he adjusted to a new role.
“Yesterday, when I told him he will play right-back, I sold the right-back idea with the captaincy,” Klopp said.
“He was already completely excited when I told him he would play right-back, and the way he executed it was super special, I have to say. Wow.Jurgen Klopp on Curtis Jones
“We thought about him because we couldn't play Stefan, we have to be careful with him. Joey will be OK for the weekend (away to Tottenham) but was not OK for today so we have to find solutions and Curtis was always in my mind as a potential solution.
“He enjoys being on the ball and the deeper you are the more often you can get the ball. It was a top performance I have to say for the first time in for him a strange position. I liked that. He's in a good moment and could probably play each position.
“But we will try to use him as often as possible in his natural position.”
Jones was one of several Liverpool players to earn praise from Klopp after their come-from-behind victory.
Dominik Szoboszlai took the headlines after hitting a superb strike to give Liverpool the lead just five minutes after coming off the bench, completing the turnaround after Cody Gakpo's goal early in the second half had cancelled out Kasey McAteer's effort, with Diogo Jota getting a late third.
“There were super signs, I really like that a lot,” Klopp said. “The boys enjoyed playing it and you saw how they were pressing until the last second. They really enjoyed it and that's cool.
“Minute by minute, we grew into that game and it was a top performance, to be honest.
“With all the quality of Leicester, we have to admit that as well, super-coached team obviously, super set-up, you can pretty much see, feel and smell the confidence they have because of their situation, so that made life difficult.
“But we kept going and improved during the game as a team clearly but individually as well, a lot of performances stepped up and here we are, and I like that a lot.”