Alexander-Arnold, who has come in for criticism lately and was dropped by England boss Gareth Southgate, fired in a trademark free-kick goal against the Gers in the seventh minute.
“A wonderful goal. What can I say? I would now say, ‘It’s Trent!’, but it’s long ago that he last scored a free-kick, so I am happy he had this still in his locker,” Klopp told reporters about the goal.
Klopp praised the England international’s overall display, insisting he has no defensive problem.
“He played a good game, defensively especially, a wonderful goal,” the German said.
“How I said, we set it up differently. We cannot talk about it every week, but Trent has no defensive problem we had a defensive problem hopefully had because our timing was not right and we take risk in defending, everybody knows that.
“If then the timing is not right, you open gaps and these gaps are very often (in) the back of Trent.
“Not because of him, but because of other situations and then he has to track back.
“Yes, how I said, we were not in the perfect moment and that’s why we just adjusted it slightly.”
The win comes amid Liverpool’s ordinary start to the Premier League season, including a 3-3 draw with Brighton & Hove Albion on Saturday.
The Reds have managed 10 points from seven league games, while they were thrashed 4-1 by Napoli, leading to criticism which Klopp insisted he didn’t listen to.
“I have no clue but the criticism is completely fine,” he said. “We are not over the moon about our situation.
“We played here some really good games it’s not like 10 years ago, it’s not too long ago and Champions League nights at Liverpool are always quite enjoyable usually. That’s what happened tonight again.
“That we were really up, I don’t think it had too much to do with the situation. The game gave us this job to do. But that’s how I said, I saw tonight a team fully committed.”