Jurgen Klopp's side were resounding 4-0 winners against Red Star Belgrade at Anfield last month to hoist themselves to the top of the group.
Milan Pavkov scored twice in seven first-half minutes to hand Red Star their first Champions League victory in 26 years.
The defeat represents a major blow to Jurgen Klopp's side, as most defeats do in fairness, who may now require maximum points from their final two group games to get through to the Champions League knockout stages.
"This is a fantastic win for our club and our nation, we have now raised the bar and have to look ways to keep improving", said Red Star's delighted coach Vladan Milojevic.
"I saw a few games like this already and it is really hard to find your mojo back".
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"It's a situation where we will go to the fantastic city of Belgrade as a football team to play football", Klopp told Liverpool's official website.
Red Star Belgrade will rely on their German veteran Marko Marin who had a failed stint at Chelsea but redefined his excellence in Serbian SuperLiga. We want the focus to be on a great game of football, free from anything else. "I'm sure we'll do that".
Maybe we are missing a bit of a spark in terms of not winning four- or five-nil in most games but if he [Klopp] thinks that then we need to try to get it back.
"I'm of the belief you start with your strongest team, get the game won and then get off the players you want to rest".
The Merseysiders played out a 1-1 draw at Arsenal on Saturday and face a crucial trip to the Serbian capital, where they will battle for three points which could be crucial to their hopes of progressing from Group C. This season we've found that a bit hard.
Robertson admitted that Liverpool's away form this term hasn't been as good as last season's but added that they are optimistic heading into the acid test against Thomas Tuchel's PSG on 28 November. "Arguably we're still to play the best team away and we need to put in a much better performance than we have done so far".