Milan Pavkov's first-half brace, which included a stunning long-range strike to make it 2-0, helped the hosts to look a different class to the side that had lost 4-0 at Anfield two weeks ago.
Group C was blown wide open with the result, the Reds having gone into the clash hoping to open up a four-point gap at the top, but a sub-par performance has put their European hopes at risk.
Asked what had gone wrong for his side in Serbia, Klopp said: “I only have 10 fingers...
“We had the first big chance with Daniel [Sturridge], a very big one. Each goal in a game like this leads the game in a specific direction.
“The atmosphere, noise-wise, was not a problem for us, but after the second goal they could smell it.
“We made it too easy for them. They deserved it with the passion they showed.”
Liverpool's performances since the start of the season have seen them tipped as both Premier League and Champions League challengers, but Tuesday's loss will raise fresh questions of continuity.
Regardless, Klopp sees the result as an isolated incident and vowed to take steps to ensure his side return to winning ways.
“We lost our mojo in the game, not in general,” he said. “We have to make sure it doesn't happen again.”
Indeed, the loss saw the Reds reach a new low, having now been defeated in three Champions League away games for the first time in the club's history.
Captain for the evening James Milner was also quizzed as to when things started to go awry, to which he replied: "From the first whistle.
"We just didn't start, and when you don't start in the Champions League, you get punished.
"We have had enough chances to get back into the game and we didn’t take them. Passing the ball wasn’t good enough.
"We need to win our games, it’s on our shoulders, we have some good sides to play and it’s in our hands but we will have to play better than we did tonight."