A first-half brace from Milan Pavkov earned Red Star all three points.
The Reds have dropped points in four of their last seven games in all competitions after a flying start to the new campaign.
The Reds are now third, level on points with second placed Chelsea and just two points behind leaders Manchester City, with all three sides still unbeaten.
A crucial miss from Daniel Sturridge in the beginning of the game set the tone for the way that Liverpool would go on against Red Star as they looked weak in defence and abysmal in attack.
"The second half was really dominant but we didn't score".
If Liverpool beat PSG, and Red Star draw with Napoli then Liverpool can lose to Napoli in the final game and still go through. For us, it was not clicking, it was not easy.
"That's the thing, not taking the chances when we're creating them". The second goal was kind of out of the blue, we had the ball and gave it away. That's not cool in a game like this, in an atmosphere like this, in situation like this, if you have to play your best football in a kind of negative mood. "It was a blow".
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That was of little concern to Red Star's players, however, as they joined arms and took the acclaim of their supporters on the full-time whistle.
The Reds are now in third place in the Premier League table and two points behind leaders Manchester City after 11 games.
"(It's going to be) very tough.
"It's one of those periods we need to get through", he said. Tonight when we saw he would play, for us it was clear it would be in a specific way different because he is a proper target player for Red Star.
"From the first whistle, we didn't start well enough, and that showed with them getting the two goals".
'We will keep going and playing because it doesn't take much for those chances to go in'.
Liverpool ideally need to get a result with a tricky tie away in the French capital to come next before a potential qualification decider at home against Napoli at the end of the group.
"I think the message it sends to the rest of the players was, 'You won 4-0 last time we'll be fine again tonight'".