The Reds' Academy graduate replaced Joe Gomez and started only his fourth Premier League game of the season but produced a mature display up against Ryan Bertrand and Nathan Redmond as the home side ran out deserved winners.
The 19-year-old has regularly swapped right-back duties with Gomez in Nathaniel Clyne's lengthy absence with a back injury this season and has scored twice in the Champions League, but Klopp felt this was his most impressive display thus far due to how well he defended.
Reds boss delighted with Alexander-Arnold's display
Asked whether the No.66's performance displayed his potential and ability after an excellent week for team-mate Gomez on England duty, Klopp replied: "I didn't need a reminder but yes, [it] probably [was a reminder] for all the rest.
"This [rotation] will happen now in the next few weeks. We have to make decisions.
"I usually don't think too much about the next game but in this case I have to think about the next 13 games. Not that I've already planned them, but we cannot play one line up and play them until they are all injured or something.
"We need to mix it up, even if we win games, like today. That's the reason [Alexander-Arnold started]. Joe had two games in the last week. That's not a problem, he could have played today but then for Tuesday, I don't think it would have been a big chance or a good idea to bring him again.
"We have Trent and he is another type of defender. When he started, he was a proper winger and sometimes a defender and now he is a proper defender and sometimes a winger. That makes much more sense in his position.
"He was really good today, I have to say. This was probably his best performance so far, over 90 minutes, in defending. What he can do offensively, everybody knows. It's so good for us that we have the two of them."
Klopp unsure on Matip injury return
Joël Matip missed out with an adductor problem, with Dejan Lovren being recalled as Liverpool's defence kept a seventh clean sheet in their last eight home games.
But Klopp is not yet sure whether Matip will be available or not for Tuesday's pivotal trip to Spain to take on Sevilla in the Champions League group stages.
"No real idea," he said when asked for a prognosis of the defender's injury. "It's the smallest strain you can have but he's a tall boy, maybe that's the problem.
"Today there was no chance [he could play], but it looks good. I don't know if he will be ready for Tuesday."