Red Star won 2-0 thanks to a brace from Milan Pavkov.
Klopp reasoned: "If you saw the first game, it was similar – it was wild, direct, stuff like that. In Liverpool we controlled the game and tonight we didn't. They were aggressive, very aggressive, in all parts – but they were aggressive in the last game as well, we only did better. We made life a bit too easy tonight for Belgrade, that's the main problem.
"As I said, they deserved it with the passion they fought [with]. In the end you have to score goals in a game and if you think about how often we were in the box and around, that's what you have to do in a game but you have to make the last decision in the right way and we didn't. That's why we lost 2-0."
The German added: "There were a lot of moments when we could get in control of the game and we didn't do it, we made the wrong decisions. I don't think that's anything to do with [playing] away or home, it just happened. We will talk about that and will do it better 100 per cent, but for tonight we can't change it anymore, unfortunately."