Match ends, Crvena Zvezda 2, Liverpool 0.
Manager Jurgen Klopp said Liverpool struggled to "find their mojo" as two early goals from Milan Pavkov gave Red Star Belgrade a shock victory in their Champions League group-stage encounter.
Victory could have taken Liverpool three points clear at the top of Group C but they dropped to second following Napoli's draw with Paris St-Germain in Italy.
Forward Pavkov headed his side into the lead after 21 minutes and fired home a powerful effort to make it 2-0 shortly afterwards.
"I saw a few games like this already and it is really difficult to find your mojo," Klopp said.
"We made life a bit too easy. I don't say it is already serious if you lose twice but we have to make sure it will not not happen again.
"We had a lot of moments when we could get in control of the game and we didn't do it, we just made the wrong decision."
Red Star dominated the first half and came close through Vujadin Savic and El Fardou Ben Nabouhane before Pavkov's opening goal.
Liverpool's Daniel Sturridge squandered a great chance from six yards out in the 17th minute.
Klopp's side had more than 80% of the possession and hit the woodwork twice in the second half but could not score as Red Star recorded their 10th clean sheet in their past 15 home games in Europe.
Qualification under threat
Liverpool were not at the races in Serbia and they were punished for it.
A hard-fought draw against Arsenal at the weekend appeared to take the stuffing out of Klopp's side as they were slow to react to the hosts' blistering start.
Sloppy passes in midfield and poor choices in attack were taken advantage of - Pavkov's second goal arrived after Liverpool had given the ball away.
Klopp was short on midfield options, given the injury to Jordan Henderson. Naby Keita was fit enough only for the bench, while Adam Lallana made just his second start in Europe since 2014.
Liverpool improved in the second half as Salah came close on several occasions but Red Star blocked everything in front of goal.
The Reds were favourites to progress from Group C before kick-off but they are still to play PSG and Napoli in their final two games so last year's finalists may face a nervous wait to see if they qualify for the knockout stages.
Damage inflicted early
Red Star Belgrade manager Vladan Milojevic spoke about how important this game was for his side before kick-off and hoped home advantage would play a big role.
Liverpool walked out to a sea of red and white and the fans' pre-arranged display was an intimidating sight.
The hosts seemed fired up by it - winger Marko Marin was shown a yellow card for protesting in the fifth minute.
Klopp also described Red Star's line-up as "the most offensive" he had seen from them in Europe this season and attack is exactly what they did.
Marin had the first shot on target - a tame one from close range after 10 minutes - and Red Star enjoyed 56% of the possession before Pavkov gave them the lead.
They could have scored earlier in the half when skipper Savic turned and fired over the bar from a corner, before Ben Nabouhane's powerful shot was palmed away by Liverpool keeper Alisson.
Red Star had scored only one goal in four and a half hours of Champions League football before they got two in half an hour against Liverpool.
It was almost a perfect evening for Red Star - who became the first Serbian team to win a Champions League group-stage game - but Filip Stojkovic was visibly frustrated as he was carted off the field with an injury in the second half.
'We have to deal with it'
Liverpool manager Jurgen Klopp: "The boys are very disappointed, I'm very disappointed and we have to do better. We have to do better because we can do better, but tonight it is too late.
"They had too many set-pieces that's true and with one of them they scored. Then more or less straight away they score the second one and then the atmosphere was completely different, you could feel it.
"They were on their bikes and we had to deal with the situation. It is not what we wanted and we will go for the other two games 100 per cent. We all have to deal with it now."
A day to forget for Liverpool - the best of the stats
- Liverpool have lost three consecutive Champions League away games for the first time.
- Pavkov became the first Serbian player to net a brace in the Champions League since Aleksandar Prijovic for Legia Warsaw against Borussia Dortmund in November 2016.
- Red Star Belgrade have won both of their European home matches against Liverpool, also triumphing 2-1 in October 1973 in the first leg of a Last 16 tie in the European Cup.
- Liverpool have lost two of their last three Champions League group games (W1), as many as they suffered in their previous 11 combined (W4, D5, L2).
- And their first shot on target of this match came in the 71st minute. The Reds failed to land a shot on target in their other away game in the competition this season, against Napoli.
Man of the match - Milan Pavkov (Red Star Belgrade)
Liverpool host Fulham in the Premier League on Sunday (12:00 GMT), before returning to Champions League action away to Paris St-Germain on 28 November (20:00 GMT).
Red Star Belgrade
- 30StojkovicSubstituted forGobeljicat 59'minutes
- 7KrsticicSubstituted forJovicicat 73'minutes
- 31Ben Nabouhane
- 17MarinBooked at 5minsSubstituted forCausicat 64'minutes
- 66Alexander-ArnoldSubstituted forGomezat 45'minutes
- 4van Dijk
- 20LallanaBooked at 36minsSubstituted forOrigiat 79'minutes
- 15SturridgeSubstituted forFirminoat 45'minutes
- Antonio Miguel Mateu Lahoz
- Shots on Target
Second Half ends, Crvena Zvezda 2, Liverpool 0.
Attempt saved. Mohamed Salah (Liverpool) left footed shot from the centre of the box is saved in the bottom right corner.
Attempt saved. Virgil van Dijk (Liverpool) header from the centre of the box is saved in the centre of the goal. Assisted by James Milner with a cross.
Joseph Gomez (Liverpool) wins a free kick in the defensive half.
Foul by Slavoljub Srnic (Crvena Zvezda).
Offside, Liverpool. James Milner tries a through ball, but Sadio Mané is caught offside.
Attempt blocked. Georginio Wijnaldum (Liverpool) right footed shot from outside the box is blocked.
Attempt blocked. Mohamed Salah (Liverpool) left footed shot from the right side of the box is blocked. Assisted by Sadio Mané.
Sadio Mané (Liverpool) wins a free kick on the right wing.
Foul by Branko Jovicic (Crvena Zvezda).
Attempt missed. Virgil van Dijk (Liverpool) header from the left side of the six yard box is just a bit too high. Assisted by Roberto Firmino with a cross.
Sadio Mané (Liverpool) wins a free kick on the right wing.
Foul by Milan Rodic (Crvena Zvezda).
Delay over. They are ready to continue.
Delay in match Dusan Jovancic (Crvena Zvezda) because of an injury.
Attempt saved. Mohamed Salah (Liverpool) left footed shot from the left side of the six yard box is saved in the top centre of the goal. Assisted by Joel Matip.
Attempt missed. Joel Matip (Liverpool) header from the centre of the box misses to the left. Assisted by Joseph Gomez.
Corner, Liverpool. Conceded by Marko Gobeljic.
Substitution, Liverpool. Divock Origi replaces Adam Lallana.