Two first-half goals from Milan Pavkov stunned the travelling Kop, and clearly too Jurgen Klopp's players as they stuttered through the rest of the opening 45.
"It's down to us, it's in our hands and we've shown that we're a very good team as well-but obviously we need to do better than tonight".
But roared on by a vociferous home support, the Serbian champions were inspired to condemn Liverpool to a second defeat in the group after also losing at Napoli last month. For many, this type of performance and result has been coming and it's ensured they will have to qualify from Group C the hard way. Last season we were scoring a lot of goals and they were going in and now they're not. They were, if you want, on their bikes and we had to deal with the situation.
Former Chelsea striker Tony Cascarino believes Roberto Firmino should be dropped by Liverpool.
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Sadio Mane had a great chance to give the visitors a lifeline, but failed to force the ball across the line from point-blank range.
An away loss to Napoli took the shine off their win but they picked up their second win against Red Star Belgrade to top the table at the half-way mark.
Red Star Belgrade have conceded just five goals in their past 14 home games in European competition, keeping nine clean sheets in this run.
Federation Internationale de Football Association fined Shaqiri 10,000 Swiss francs ($9,951.24) for the gesture, along with team mate Granit Xhaka, another ethnic Albanian of Kosovar heritage, who scored Switzerland's equaliser in the same game and celebrated with a similar signal.
Left-back Andy Robertson, playing nearly as an out-and-out winger after the break, saw a cross deflected on to the top of the crossbar, while Salah finally forced a save out of Milan Borjan, hitting a post with his next effort.