It's all going a bit wrong for Klopp's side and one Liverpool fan flawless summed up all the issues from the game in one tweet.
With the confidence flowing, Pavkov then doubled Red Star's advantage six minutes later, holding off the challenge of Georginio Wijnaldum before steadying himself and firing home from 25-yards out.
"I dedicate this win to our supporters", said Vladan Milojevic, the Red Star coach.
Victory would have had Liverpool sitting pretty, regardless of the group's other result later in the day. "They were phenomenal. They live for this, we live for this". So they could score that one and, out of the blue more or less, they scored the second one.
"As players, we've got to take full responsibility and make sure it doesn't happen again", Lallana told LFCTV. The Reds have to play PSG and Napoli in their final two games, and they'll likely need at least four points to feel good about their chances. It is not what we wanted and we will go for the other two games 100 per cent.
"I saw a few games like this already and it is really hard to get your mojo back".
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The Serbian side scored twice in the first half to give Klopp plenty to talk about at the break but the Liverpool manager was unable to motivate his players to come back and cause any late drama at the Stadion Rajko Mitic.
The scoring boots were off for Liverpool in a game the team expected to win.
"It was a slow start all round really and we gave them far too many opportunities, especially from set-pieces", Lallana continued.
'We have all our emotions after a game, but disappointment and frustration is not advisable. They deserved it with the passion they showed.
Reacting after the encounter, Klopp was unhappy his side could not hold their own against their hosts and insists they must step up the ante for their game which is trip to Paris to battle Ligue 1 giants PSG later this month.
Red Star moved onto four points, two behind Liverpool, and its home form means it still has a chance of a top-two finish.
Jurgen Klopp's men have now lost three consecutive top-level European away games for the first time since 1979.