Alexandre Lacazette put Arsenal in front in the 25th minute but the Premier League champions took control of the game and emerged as comfortable winners with goals from Andy Robertson, Sadio Mane and Diogo Jota.
Arsenal did have a number of chances though, something which Keane pointed out on punditry duty for Sky Sports.
This appeared to annoy the Liverpool boss.
"Did I hear right that Mr Keane say we had a sloppy performance tonight, because I could hear you already?" Klopp said.
"Did he say that? This was a sloppy performance tonight? Maybe he spoke about another game. It cannot be this game, sorry.
"That's an incredible description of this game. This was absolutely exceptional. Nothing was sloppy, absolutely nothing. It was, from the first second, dominant against a team in form, 100 per cent in form.
"About this game tonight, there is nothing bad to say."
"I think you might have misheard me," replied Keane. "I said there were sloppy moments but I think you have been outstanding.
"I've been giving the club nothing but praise. I'm not sure you heard me correctly there. You need to hear the rest of it."
"I will, 100 per cent," Klopp replied as both men laughed the incident off.
