Liverpool were on the backfoot for the majority of the game but found themselves level at the break, with a scrappy Gabriel own goal cancelling out Bukayo Saka's opener.
However, a disaster at the back gifted Gabriel Martinelli a second for Arsenal, before Leandro Trossard condemned the Reds to defeat in stoppage time by adding a third to the tally.
While admitting that the better team came out victorious, Klopp has taken issue with the circumstances surrounding Konate's dismissal, which saw him sent off for two bookable offences.
"In general we can admit that Arsenal deserve the three points," he told Sky Sports.
"A lot of things were against of us today. This referee gave me a red card against Man City for wrestling situation between Bernardo Silva and Mo Salah. Today same situation with Jota but didn't get a red card.
"It is unbelievable, then the of holding Havertz on Konate for the first yellow card. Havertz goes down and the referee gives Konate a yellow card.
"Gabriel does the same to Nunez and no yellow card."
The Reds were particularly lacking of attacking firepower at the Emirates - something which coincided with the relegation of Darwin Nunez to the bench, after Klopp revealed that the Uruguayan had been nursing a foot injury.
The fact he was fit enough to make the bench has left people questioning whether the striker should have started, given his fine form as of late.
However, Klopp has stuck to his guns and believes Nunez's absence from the starting XI was not the defining factor of the outing.
When asked if leaving Nunez out was a mistake, Klopp said: "Maybe. But I understand it.
"We did not play enough football. We were not involved in the game enough, we wanted Trent more on the wing.
"Would I do it again like that? Yes."