The Danish outfit were undone by Arturo Vidal, the Chilean's hat-trick leaving Copenhagen bottom of Group B and unable to qualify for the knockout stages.
Vidal struck the first from the penalty spot in the 29th minute before the visitors drew level 11 minutes into the second half through former Juve man Olof Mellberg.
However, Mellberg then brought down Fernando Llorente five minutes later to allow Vidal to convert his second penalty, before the midfielder looped a header into the net to complete his hat-trick and seal a first win of the campaign for the hosts.
After the game, Jorgensen was in a desperate mood.
"I feel quite bitter right now," he said. "I'm annoyed by the defensive mistakes. I feel that we could have got more out of this match.
"We could have got at least a point. We created too few opportunities as well."
Copenhagen will round their Champions League campaign off when they host Real Madrid on December 10, where a win will secure UEFA Europa League football in the new year.
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