Just ten minutes into the encounter Van Dijk was forced off injured after Pickford clattered into him as he attempted to get on the end of a cross.
It later emerged that the Reds defender will require surgery on his knee, and he looks set for a lengthy spell on the sidelines.
Pickford escaped without a card from the incident but there were some suggestions he could receive a ban at some point this week.
However, according to The Athletic the fact that VAR did review the incident at the time but deemed it not worthy of a red card means retrospective action is unable to be taken.
Liverpool are believed to be furious with the way VAR was used during the derby, with a late Jordan Henderson ‘winner’ being ruled out despite Sadio Mane appearing to be onside adding to the sense of injustice.
Reds officials have made a formal approach to the Premier League, with a demand for a review of how the video assistant referee system was implemented during the game.
Van Dijk, meanwhile, has sent a message to supporters insisting he will do everything he can to try to return to the pitch as soon as he can.
He took to Twitter on Sunday to write: “This afternoon I met with a leading consultant to start the process of planning the finer details of my rehabilitation following the incident yesterday.
“I’m now fully focused on my recovery and will do everything I can to be back as quickly as possible.
“Despite the obvious disappointment, I’m a firm believer that within difficulty lies opportunity and with God’s help I’m going to make sure I return better, fitter and stronger than ever before.”
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