Gary's younger brother, Phil, was on "Match of the Day" on Sunday and urged Karius to "Keep your mouth shut, do your job" after the shot-stopper made a difficult 2-2 draw with West Ham United.
Former Manchester United defender and Sky Sports analyst Gary Neville was critical of Karius following mistakes made in last week's 4-3 defeat to Bournemouth, which prompted Karius to hit back at him in an interview with the Daily Mail.
Klopp came to the rescue
"The pundits are former players and a lot of them forgot obviously completely how it felt when they got criticised -- and especially the Neville brothers," Klopp told a news conference at Melwood on Monday.
"I have to say the one who was a manager [Gary], he obviously should know that too much criticism never helps but he's not interested in helping a Liverpool player I can imagine. "But that makes the things he says not more sensible. He showed he struggled with a job to judge players, [so why do] we let them talk about players on television?
"The only thing I can do is I don't listen to them. I'm pretty sure Carra [former Liverpool defender and Sky Sports pundit Jamie Carragher] doesn't speak too positively about Man United players, and obviously the Neville brothers don't like Liverpool and if they can cause bigger problems than we already have, I think they'll try it -- that's all."
"Now you have your headline, you're welcome. You should have asked the right question earlier. "By the way, you can tell him I'm not on Twitter, so if he wants to tell me something, Twitter doesn't help."
Says he protects his players as much as possible but could not control what they do when they go out onto the pitch
"That's part of our life," he said. "First of all, my job is to protect the players as much as I can in different situations, but they are alone on the pitch, I cannot go with them and say now left and now right.
"We have to prepare ourselves as much as possible. It's a normal situation -- to have criticism from outside, it's normal for me, for my players, for the goalkeepers. "We all wish it would be different, but it's not. I'm not surprised about it -- in my very first press conference, I spoke a little bit about the English media and obviously most of you enjoy it a little bit being this harsh part."