Alexander-Arnold was turned too easily by Marcus Rashford, who lashed into the far corner to give United the lead before the England forward took advantage of more haphazard defending from Liverpool to double the Red Devils' advantage.
An Eric Bailly own goal gave Liverpool hope but they could not complete a second-half comeback at Old Trafford, with club legends Jamie Carragher and Graeme Souness taking aim at Alexander-Arnold.
Klopp, though, has no interest in their thoughts on the teenage right back.
Asked about their comments, he said: "I don't get it. If you wouldn't tell me [about it], I would never watch it. That makes absolutely no difference to me, what people say.
"What did they say? They said we defended bad? If somebody said it was only Trent's mistake, then the guy who said that has no idea about football and I wouldn't listen.
"Dejan Lovren, in the first challenge, could be different, but it's difficult. We were not there for the second ball and then it's Trent.
"I have to see it back again but when I saw the goal, for me Rashford did brilliantly and, exactly in the moment where Trent is ready for the challenge, he made a cut back.
"He stepped too late and in the next moment he shoots. It's the perfect striker movement and we cannot defend everything.
"It's easy afterwards to talk about it but I'm not interested. [Pundits] don't give us points, they don't cost us points, they are only the deliverer of good and bad messages, that's all.
"We lost 2-1, but everybody could see we're strong. We brought them at the edge, with 2-0 down that's really rare that you can turn a game against United, but we were close and actually we should have done it."