Reds boss Klopp is furious the Neville brothers have been so negative in their opinions about the error-prone Karius and on Monday he took the opportunity to put them in their place.
Following Liverpool's recent 4-3 Premier League defeat at Bournemouth, Gary Neville said Karius, a pre-season signing from Mainz, transmitted anxiety to his defenders after he fumbled a shot that allowed Nathan Ake to score the late winner.
Karius responded by blasting Neville in an interview, saying of an unsuccessful spell with Valencia: "He was a manager for a short bit and now he is back to being an expert again".
Phil Neville came to his brother's defence on the BBC's Match of the Day highlights programme when he said Karius should "keep his mouth shut and do his job".
Karius came under more scrutiny after his mistake led to Dimitri Payet scoring a free-kick in Sunday's 2-2 draw with West Ham United.
But Klopp was quick to defend his goalkeeper in a remarkable tirade about the Nevilles, who have few friends at Anfield after their long association with arch rivals United -- while Phil also had a long spell at Everton.
"The pundits, former players most of them, forgot completely how it felt when they got criticised," Klopp said at a press conference ahead of Wednesday's match against Middlesbrough.
"Especially the Neville brothers: the one who was the manager (Gary), he obviously should know that too much criticism never helps.
"But he is not interested in helping a Liverpool player, I can imagine, but that makes the things he says not make more sense.
"He showed he struggled with the job to judge players when he was manager, so why do we let him talk about players on television?
"I don't listen to them. Obviously the Neville brothers don't like Liverpool, I have no problem with that and if they can cause bigger problems than we have already they have tried."
Asked if Karius would remain in goal against Middlesbrough or if Simon Mignolet would be recalled, Klopp tried to side-step further controversy.
"I am absolutely not interested in creating headlines so you can write what you want," he said.
"First of all my job is to protect the players as much as I can but I am not in the pitch so I cannot go with them.
"There is nothing to say about it. A few things are obvious, a few things are not obvious, a few things are the truth, a few things are not right but that is too much for me to think about."
And in a parting shot to Gary Neville, who regularly expresses his opinions on social media, Klopp added: "By the way, you can tell him I am not on Twitter so if he wants to tell me something Twitter doesn't help."