The Reds boss made five changes to his starting line-up for the visit of the Serbian champions in Group C and was rewarded with a comfortable win secured through goals from Roberto Firmino, Mohamed Salah (two) and Sadio Mane.
Fabinho was among those to come into the team, for his second start since signing in the summer, while Adam Lallana, Alberto Moreno and Daniel Sturridge got minutes off the bench at Anfield.
But Klopp felt the non-use of the Liverpool vice-captain perhaps best showed the quality of the options at his disposal throughout the squad.
“I said it immediately in the dressing room: we could rest James Milner!