The Italian side scored two quick-fire goals to pull off a surprise 2-0 win over the Premier League champions at Anfield.
Atalanta piled pressure onto the Reds, leaving them with only three off-target shots on goal to show for their efforts.
And it seems it all became too much for the manager when the lead was doubled after 64 minutes.
Josip Ilicic had just poked the ball into the back of the net four minutes earlier, leading the German boss to bring on Fabinho, Andy Robertson, Roberto Firmino and Diogo Jota.
But they could not stop Alejandro Gomez looping in another cross, with Hans Hateboer beat Joel Matip to in the air to give Robin Gosens a tap-in.
While the Italian side celebrated, there was an awkward silence around the empty Anfield ground.
Klopp, though, was heard shouting to his dejected players: “Please, start playing football boys.”
Liverpool’s defeat to Atalanta was their first loss in eight games, the last being the 7-2 hammering by Aston Villa.
And it saw the Reds boss take aim at referee Carlos del Cerro Grande for his management of the game.
Speaking to BT Sport after the game, Klopp said: “It was not a good game. From both teams, didn't create a lot, until they scored the goals.
“A deserved defeat in a difficult game. The ref didn't whistle a lot and that makes it even more difficult, for both sides. It was unbelievably intense and you need some breaks.
“When the first half is gone, you usually settle but for some players who didn't play for a while it was very intense for them. We didn't find a way in the game.
“Easier to talk about a good game. We had moments but not real chances. It could happen to other teams.
“You ask us to go Saturday at 12:30, which is nearly a crime. That is nothing to do with the result, but congratulations to you.
“Thumbs up, no injuries and we go again.”
But there has been good news for the Reds, though, as the new tier system will allow 2,000 fans into Anfield after December 2.