His team were outplayed for swathes of the contest, but an angry Klopp's main focus in his post-match interviews was on the performance of the official.
The Pole issued six yellow cards to Liverpool and two to PSG - one of which, for Marco Veratti's foul on Joe Gomez, the Liverpool boss was adamant should have been a red.
And the German was further angered by the referee's apparent uncertainty about awarding the penalty from which Liverpool scored through James Milner, with the assistant referee influencing the decision.
"We have six, seven, eight yellow cards and we were close to a red card.
"Yes, there were one or two holding things which were yellow cards, but all the others - it's unbelieveable.
"We got a penalty - the ref didn't want to give it but I don't know how that's possible.
"The ref needs to be prepared for a game like this and he looked not prepared.
"But they scored two and we only [got] one so it's our fault."
He continued on the same theme in his press conference, adding: "That was a red for me, clearly from Veratti. I saw it very well and for sure it was not the same colour card as the 500 we got tonight."
Asked if the official had been infuenced by apparent play-acting by PSG star Neymar, Klopp snapped: "It's not for me to talk about Neymar."
And he added to his interviewer: "Ask the ref. You can. Try."
Despite his anger, Klopp says his side remain confident of reaching the knockout stages ahead of a do or die test against Napoli.
"Napoli is unbelievabley strong and we have to win by two goals which is not an easy job but we'll have Anfield at out backs and we still believe," he said.
"We are dispoointed, for sure but we'll have to be spot on."
Liverpool return to action on Sunday when they host Everton in the season's first Merseyside Derby.