Liverpool are outside the top two positions of Group C following Wednesday's 2-1 loss in the French capital.
The Reds were unable to add another name to the scoresheet after James Milner's penalty on the stroke of halftime, meaning Paris Saint-Germain took all three points through earlier goals from Juan Bernat and Neymar.
The result could have been very different, however, if Marco Verratti - who was a livewire in central midfield for PSG - was sent off for a challenge on Joe Gomez just 24 minutes into the Champions League scuffle.
Liverpool have lost each of their three away matches in a Champions League group for the first time, and they mustered just one shot on target across their trips to Napoli and Paris Saint-Germain. The other defeat, a 2-0 reverse at Serbian outfit Red Star Belgrade, is arguably the biggest shock of the current continental campaign.
Napoli sit atop Group C with nine points, while Paris Saint-Germain have collected eight points. Liverpool and Red Star round off the quartet with six and four points, respectively.