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.
Goalkeeper Alisson Becker was forced to save low to his left after El Fardou Ben Nabouhane's shot from distance, but, from former Chelsea midfielder Marko Marin's resulting corner, Pavkov headed home. In this case goal difference will come into play between Liverpool and Red Star Belgrade.
Milan Pavkov scored twice in the first half to hand the home side the victory and increase the competition in Group C heading into the fifth and six games of the group stage.
"That's the thing, not taking the chances when we're creating them".
However, it would be preferable to avoid a nail-biting Anfield finale which would require them to beat the Serie A side by two goals to overturn their head-to-head record against Carlo Ancelotti's team.
Yet, even while Liverpool's results have remained positive, they have rarely been accompanied by the level of performance they achieved on their run to the Champions League final last season.
"In the second half we were better, we had enough chances to get back into the game and we didn't take them and you get punished".
Liverpool tried to force their way back into the game and came close through Robertson and Salah.
"The atmosphere, noise-wise, was not a problem for us, but after the second goal they could smell it".
And Klopp has warned his squad that they can not afford to let slip any more points if they want to make it through to the last 16. We have a long flight home and have enough time to think about it.
Then Pavkov, Red Star's talented young striker, went off. 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.
They didn't give up fighting, they stayed concentrated and they gave everything. 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. "They deserved it with the passion they showed".
Liverpool's terrible display in their defeat to Red Star Belgrade on Tuesday night can be summed up in one statistic - zero succesful tackles in midfield.