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. It was reported that a dispute between Buvač and Klopp was the reason behind his decision to leave, but it remains unclear.
Red Star drew 0-0 with Napoli in its previous home game. So they deserved the three points.
A damaging 2-0 defeat to Red Star Belgrade in Serbia sealed Liverpool's worst away run in Europe's elite club competition in 39 years and made qualifying from Group C that bit harder.
Speaking in his pre-match press conference, the German tactician said, "We will take pretty much everyone". Four points from their last two games would be enough to guarantee the Reds' progress to the last 16.
Liverpool had a lucky escape at the start of the second period - the referee failing to award Red Star a penalty when a shot struck the arm of James Milner.
The Reds are now third, level on points with second placed Chelsea and just two points behind leaders Manchester City, with all three sides still unbeaten.
"Everyone looks at Liverpool in a different way, always expecting great games and many goals". Before that, Liverpool had scored in 14 straight games.
"In the second half I thought we did better, obviously, we had enough chances to get back into the game, but we didn't take them and you get punished".
Speaking of the Switzerland international's situation, the manager said, "We have heard and read the speculation and talk about what kind of reception Shaq would receive and although we have no idea what would happen, we want to go there and be focused 100 per cent on football and not have to think about anything else, that's all".
Almost three decades on, Red Star don't have a household name in their squad and needed to qualify for the group stage through the playoffs.