With Joel Matip unavailable and Nathaniel Clyne injured, the 18-year-old was handed his first top-flight start on a big occasion at Old Trafford on Sunday.
And Alexander-Arnold’s efforts delighted Klopp, whose side drew 1-1 after Zlatan Ibrahimovic’s late header cancelled out James Milner’s first-half penalty.
Klopp: United resorted to long balls
“It was an outstanding performance,” Klopp told reporters after the match.
“It is good to have him and show him to our Liverpool supporters. The right-back spot is in good hands even when Clyne is not available.
“Immediately against a player like [Anthony] Martial, one of the quickest players in the Premier League, he needed a few minutes to adapt to the game but then he did very well.
“What a boy. I could have played Milner right and Alberto Moreno left but I didn’t want to change two positions. We thought he is ready for it.
“We had a very positive performance. We were the better side, played the better football, had a better plan. We changed the system a little bit and obviously had line-up problems.
“The boys did really well. Unfortunately we only scored with a penalty - there were other situations where we could have been a little bit more clinical to score.”
United boss Jose Mourinho and Klopp went head-to-head on the touchline in stoppage-time after a clash between Roberto Firmino and Ander Herrera resulted in bookings for both players.
“I think he wanted a minimum yellow, I don’t know,” said Klopp.
“It should have been a yellow card just for Herrera. At the end it was a yellow card for the guy who wanted to play football. We could not have the same opinion at that moment.”