The Anfield encounter pitted the league-leading Gunners against the third-placed Reds, who had been overtaken by Aston Villa courtesy of the Lions' stalemate with Sheffield United on Friday evening.
Klopp's side were caught cold with just four minutes on the board, though, as Arsenal's explosive start was rewarded when Gabriel Magalhaes headed home from Martin Odegaard's free kick.
Liverpool were only behind for 25 minutes, though, as a sumptuous cross-field pass from Trent Alexander-Arnold found Mohamed Salah, who comfortably evaded the attention of Oleksandr Zinchenko and fired home into the roof of the net after cutting inside onto his left foot.
However, the Reds felt that they should have been awarded a penalty for handball before the half-time whistle blew, as the ball clearly struck Odegaard's arm inside the penalty area, but their appeals were waved away.
Odegaard appeared to be using his arm for leverage as he slipped on the turf, and the VAR room also concluded that the Arsenal captain was trying to move his arm towards his body rather than away from it.
Chris Kavanagh's on-field decision and the subsequent VAR review did not go down well with Klopp, who also took a swipe at former referee Dermot Gallagher, claiming that the 66-year-old will find a way to defend the officials' conclusion in his Ref Watch segment on Sky Sports News.
Speaking to the media after the game, Klopp said: «I think we all agree it was handball. I always wait until Mr Dermot explains it to me the next day what's really the case. He will find a way to explain to me that it wasn't
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