Red Star Belgrade have thrown Champions’ League Group C wide open and loosened Liverpool's grip on top spot after Milan Pavkov scored a first-half brace in a 2-0 win.
Pavkov broke the deadlock 22 minutes in with a towering header from Marko Marin's corner after evading the attention of Virgil van Dijk.
The striker soon got his second, shrugging off Georginio Wijnaldum and beating Alisson with a fierce 25-yard drive to leave Klopp looking stunned on the touchline.
Salah and Van Dijk wasted late chances, as Red Star dug deep to open the door to Napoli or Paris Saint-Germain in the hunt for first place.
A victory would have had Liverpool sitting pretty, in spite of the group's other result later in the day. However, defeat means they cannot really afford to lose either of their two final round-robin games against PSG and Napoli, who are both impressive sides.
Klopp opted to rest Roberto Firmino and give Sturridge a rare start.
Liverpool are next in Champions League action away to PSG on November 28 after Premier League outings against Fulham and Watford. Red Star travel to Napoli on the same day following domestic encounters with Dinamo Vranje and Radnicki Nis.
This article was most recently revised and updated 5 years ago
