The defeat represents a major blow to Jurgen Klopp's side, as most defeats do in fairness, who may now require maximum points from their final two group games to get through to the Champions League knockout stages. They last played in the European Cup in 1991 as holders, when beating the likes of Liverpool would not have been regarded as such a surprise.
Red Star scored two quick goals in the first half, while Liverpool missed several guilt edged chances to get back into the game.
That was of little concern to Red Star's players, however, as they joined arms and took the acclaim of their supporters on the full-time whistle.
Liverpool head to a potentially tricky away tie against Red Star Belgrade knowing full well that a victory would give a significant boost to their qualification hopes. And from the resulting corner, the home side were in front. Fearing Tuesday's clash as the potential stage for political statements to be thrown around due to Shaqiri's mere presence at Stadion Rajko Mitic, Liverpool have taken the precaution of leaving Shaqiri at home to avoid the midweek clash becoming the venue for anything other than a Champions League game. Andrew Robertson's deflected ball in came off the crossbar before Mohamed Salah's effort struck the post. We've got the experience of playing in these stadiums before and we're just to focus on the game at hand.
`Man eater` tigress Avni killed in Maharashtra
Women and Child Development Minister Maneka Gandhi on Sunday lashed out at the BJP-led Maharashtra government for killing Avni . Gandhi also expressed concern over the well being of the two cubs left behind after the killing of their mother.
Liverpool would have been four points clear at the top - for at least a few hours - had they won, but their inability to do so means Napoli or Paris Saint-Germain can overtake them. Liverpool try to turn home the rebound but it won't quite drop for them and Red Star hack it to safety.
"We have heard and read the speculation and talk about what kind of reception Shaq (Shaqiri) would receive", Liverpool manager Juergen Klopp told the club website.
They got a hard group stage draw when PSG and Napoli came out of the hat with them but they continued their excellent European form with an opening round win against the Ligue 1 champions to put themselves in pole position.
Meanwhile, Monaco were handed a humiliating defeat that all but ended their Champions League campaign as Thierry Henry once again failed to secure a maiden win as coach.
He scored his first goal in a 4-1 win over Cardiff City last month.