Westerveld was reacting when calling the derby for Dutch television and was shocked by not only Pickford's actions - but that the England goalkeeper escaped any action, let alone a red card.
It's since been confirmed Van Dijk will undergo knee surgery after he was forced from the pitch just minutes after being clattered by Pickford.
On the day, Westerveld said on the Voetbal International Talk Show via Voetbalzone: "This was really an attack. You block the ball on the back line (as a goalkeeper), but you don't jump in with scissors. He really flies in at knee height, unbelievable.
"Outrageous! I almost want to say: I can't sleep on it. It's inconceivable that it happened."
Westerveld was stunned Pickford escaped dismissal, reasoning that if the referee had been clattered after the whistle had been blown - as what occurred at Goodison Park - action against the player would still have been taken.
The Dutchman continued: "If I give the referee an elbow after the whistle is blown, it doesn't matter if it happened after it is blown? He should have had a red card for this. If I have to believe the reports, he (Van Dijk) will be out for at least six months."
- updated October 19