The 19-year-old was in fine form as the Reds carved out a commanding aggregate lead in the first leg of the sides' Champions League quarter-final, brilliantly shackling the dangerous Leroy Sane over 90 minutes.
And Klopp was delighted to see the young defender put on such an impressive showing on the biggest stage.
He told Liverpoolfc.com: "He did brilliant. He got criticism after [Manchester] United and after Crystal Palace - not internal but people are always quick with that.
"But then the best thing is to respond in a football way and that is obviously what Trent did. I was happy for him that he could show that performance.
"It's really pretty rare that Sane had pretty much nothing for finishing, making goals, stuff like that. It was outstandingly good, to be honest."
Alexander-Arnold was not the only Academy graduate in the Reds' squad yesterday evening, with teenager Conor Masterson drafted onto the bench as defensive cover.
On the Dublin-born centre-back's inclusion, the boss added: "For the boys it's nice of course.
"To be absolutely honest, I was happy that we didn't have to use Conor yesterday because first game a Champions League game against Manchester City, that's not the start you wish for!
"Probably the boys want to do it but that's a proper challenge then. So it's all good and that he's around is really good."
Klopp also confirmed that there are 'no issues' with Roberto Firmino's fitness after the striker was withdrawn 71 minutes into the win over City.