Klopp wanted clarification from Roy Keane after hearing the former Manchester United captain describe aspects of Liverpool's game as 'sloppy'
Liverpool ran out 3-1 winners at home against Arsenal on Monday night in the Premier League.
A bad mistake from Andy Robertson during the first half of the game allowed Alexandre Lacazette to open the scoring but the Reds quickly pounced back from the setback through Sadio Mane and Robertson with new boy Diogo Jota scoring the third in the closing minutes of the second half.
Keane after the game suggested Klopp might have been unhappy with one or two defensive moments from his team.
The former Manchester United midfielder said on Sky Sports: "They're like a machine.
"They've got great quality going forward. They're obviously one of the fittest teams around. They suffocate teams. I know Arsenal were encouraging them by playing out from the back but they have loads of goals in them.
"They were sloppy on one or two occasions at the back but job done and a good start to the season for them."
Keane's last comment, however, provoked a spiky response from Klopp.
“Did I hear it right, that Mr Keane said it was a sloppy performance tonight?" he asked. "I could hear you already, did he say that?"
Keane replied: "I think they gave up one or two opportunities which they will be disappointed with."
"I just wanted to hear it,” he said. “I’m not sure I heard it right, maybe he was speaking about another game… it cannot be this game, sorry!
"That is an incredible description of this game, that was absolutely exceptional. Nothing was sloppy, absolutely nothing.
"From the first second, we were dominant against a team in form, 100 per cent in form. You have to be careful like hell and not get counter-attacked. I think 60 or 70 per cent of all the balls in behind were offside. You have to wait a little longer for the flag now so that's why it feels not great, but they were offside.
"Alisson had to make one save, they had two balls in behind, you cannot avoid that. You need a goalie in these situations. Apart from that, the football we played was absolutely exceptional tonight.
"About this game tonight, there is nothing bad to say. It was the opposite of sloppy."
Keane did get in one final barb after Klopp had left, remarking: "Very sensitive, Jesus. Imagine if he'd lost!"