Juan Bernat and Neymar, whose 31st goal in the competition saw him leapfrog Kaka as the top-scoring Brazilian, put the hosts ahead before James Milner's penalty on the stroke of half-time offered hope.
Marco Verratti was running the game in midfield, although the Italian was fortunate not to be sent off for a risky tackle on Joe Gomez midway through the first half. "It can happen", said Van Dijk.
Neymar and Kylian Mbappé ran riot through the Reds' defence, handing Jurgen Klopp's men a third loss in the European campaign, at odds with their domestic form in which they are yet to taste defeat.
"There was a clear red card exactly in front of me from [Marco] Verratti".
Just six months after reaching the Champions League final against Real Madrid in Kiev, Liverpool could find themselves in the Europa League in the second half of the season, but Milner said that the team will not merit a place in the knockout stages if they are unable to defeat Napoli.
There's every chance the former three time Champions League victor knows exactly what he's doing when he says their game on Monday will be more hard as he tries to make sure his players don't lose focus on the league game.
"The penalty, I have no idea why it was a late decision. Then it's the 11th of December, we have a proper final at Anfield".
And Milner feels the Merseyside derby is the flawless game to get back to winning ways.More news: SF Giants Owner Donates To Controversial Senate Candidate
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"He didn't even whistle a foul". But it was an important game and everybody tries to do it like that.
"When the game starts like that, it's quite hard to gain confidence always", he said.
"We must go to Anfield with courage and play our game".
"Now we have to use Anfield one more time".
"The little hurdle was the 5,000 interruptions tonight, but the referee still thinks he did everything right", he added.
"We have won the fair play league twice in England but we looked like butchers when you see the yellow cards we had".
"They were constantly down, which made the boys aggressive, which does not help".
Much has been made of PSG's theatrics during Wednesday's clash at the Parc des Princes, with Milner penalised by the referee on a number of occasions.