Ki-Jana Hoever also made his first start for the Reds, eight months on from his debut in the FA Cup at Wolves, and netted the second goal after a brilliant cross from James Milner, who opened the scoring in Milton Keynes.
It was Curtis Jones who picked up the Man of the Match award, but equally impressive on the opposite flank was Elliott, who hit the bar twice in an excellent debut.
Speaking in his post-match press conference, Klopp praised the 16-year-old’s display, and stressed that it is “important we can give [young players] these matches.”
“Sixteen years old, this kind of football…it’s good. Brilliant boy, takes these situations really well,” he enthused.
“He will always be a special player for moments, but his overall performance, defending, his moments, it’s not easy to play.
“That’s really, really good, and his left foot is not bad. Bit unlucky, otherwise he would have scored.
“Good player. They are all good, we can’t have bad young players, they are all really skilled.
“That’s why it’s important we can give them these matches, and we will try to continue like this.”
Hoever endured a difficult game defensively, but rose highest at the right moment to power home Milner’s delivery in the 69th minute to become the fourth-youngest goalscorer in the club’s history.
Klopp, who began his senior career at Mainz as a right-back, assessed the Dutchman’s evening he described it as “quite impressive” how he coped.
“Ki-Jana, I didn’t play when I was 18 on a similar stage, so it was quite impressive,” he said.
“The first half was very, very defensive orientated, then he was needed in the other box and he was there. Wonderful cross, wonderful goal.”
Asked whether he saw Hoever as a right-back or centre-back in the long term, the manager was rightly cautious to put any labels on the 17-year-old.
“There’s no reason to decide that now,” he responded.
“He can play both but the full-back is a little better for him in the moment. We have to see how he develops physically.
“He has the speed, passing quality, crossing can be improved, but [he has] a lot of skills that are useful at full-back.
“But that has to be more natural, his desire to go in the right direction, open up, control the pass and see the pitch.
“It’s only 17 years old and if they can’t improve any more that would be strange.”
Elsewhere on Wednesday night, a very young Liverpool under-21s held Fleetwood Town to a 1-1 draw in the EFL Trophy, but were then beaten on penalties to award an ‘extra point’ to the hosts.