Jurgen Klopp decided to make some changes from the side that drew at Arsenal last weekend with Lallana coming in for Fabinho in midfield while Daniel Sturridge was also preferred ahead of Roberto Firmino up front.
The match was turned on its head in the 22nd minute when Milan Pavkov headed in from a corner.
A first half brace from Milan Pavkov did the damage, with Liverpool failing to cause their Serbian opponents any major issues at the back. We made life a bit too easy tonight for Belgrade, that's the main problem.
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Roberto Firmino says Liverpool have the strength in depth to challenge Manchester City for silverware this season.
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. But the atmosphere after the second goal especially, in the whole club, if you want, they could now smell it. However, defeat means they can not really afford to lose either of their two final round-robin matches against PSG and Napoli, who are both impressive sides. The visitors give possession away cheaply once more and they are in deep trouble now. At half-time we walked a long way to the dressing room and they were all in a very positive mood. In Liverpool we controlled the game and tonight we didn't. Arsenal are 1/3 to win the match and that looks a fair price but an Arsenal win and more than 2.5 goals to be scored must be considered at 5/6.
And Red Star doubled their lead just seven minutes later when Pavkov bagged his second with a superb strike from 25 yards out which Alisson may feel he could have done better with.
"From the first whistle, we didn't start well enough, and that showed with them getting the two goals".
If Liverpool draw with PSG and Napoli draw with Red Star, then Liverpool will need to beat Napoli in order to go through, or draw with them and hope that Red Star get a result against PSG.