The Frenchman has sparked outrage in his homeland after making the gesture but insists it was a tribute to comedian friend Dieudonne and not a right-wing endorsement.
The former France international performed the action after scoring his first of two goals against West Ham on Saturday, causing uproar in his homeland.
Anelka tweeted after the match that he acted in tribute to his friend Dieudonne M'Bala M'Bala, a controversial comedian, who himself claims the gesture is anti-establishment rather than anti-Semitic.
France's minister for sport, Valerie Fourneyron, branded the act "disgusting", with many in France deeming the gesture a reverse Nazi salute.
Anelka has again taken to Twitter to defend himself, urging people not to be fooled by varying definitions suggested by members of parliament and circulated online and in newspapers.
"Meaning of quenelle: anti-establishment. I don't know how the word religion has come to be a part of this," he said. "This quenelle was a dedication to Dieudonne. Concerning the ministers who have given their own interpretation of my quenelle, they are the ones who create controvery and confusion without knowing what the gesture really means.
"I ask people not to be duped by the media and, of course, I'm neither antisemitic or racist."
The FA has confirmed that it will investigate the celebration, with Anelka facing at least a five-match ban if found guilty of anti-Semitism.