Liverpool face an uphill task to qualify for the knockout rounds of the Champions League after suffering a 2-0 defeat away to Red Star Belgrade.
Milan Pavkov scored both goals as the Group C's basement club picked up their first win of the competition to give themselves hope of continuing in Europe.
Liverpool still have Napoli and Paris Saint-Germain to play and must now do it the hard way to finish in the top two.
But Liverpool should have been in front in the 17th minute when the ball ran kindly for Daniel Sturridge inside the six-yard box, but the England international somehow managed to blaze over the bar when completely unmarked.
A few minutes later El Fardou Ben Nabouhane, Red Star's top scorer, brought a fine save out of Alisson with a powerful drive from long distance. And from the resulting corner, the home side were in front.
Marko Marin delivered from the right-hand side, and Pavkov -- who had never before scored in the Champions League -- rose unmarked to nod into the bottom corner on 22 minutes.
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.
Adam Lallana almost got Liverpool back in the game moments later but his header was deflected just wide, and Sturridge then fired wide from just inside the box.
The visitors nearly got lucky 10 minutes after half-time when Andrew Robertson's deflected cross bounced back off the top of the crossbar.
Liverpool continued to dominate the ball as Red Star sat back, and Mohamed Salah went close when his 71st-minute effort went behind off the outside of the post.
Joel Matip failed to connect with a lofted ball into the box, then Salah failed to get decent purchase on the loose ball as time ticked down. Virgil van Dijk then headed onto the roof off the net from 10 yards out.
Salah had the last effort deep into stoppage time, shooting straight at goalkeeper Milan Borjan.
There was to be no way back for Liverpool as the Red Star fans celebrated a famous victory.