... asked people not to be "duped by the media".
The striker caused a storm in his native France by performing the 'quenelle' salute made famous in his homeland by comedian Dieudonne M'Bala M'Bala after scoring the first of his two goals at Upton Park in the 3-3 draw.
The gesture has been linked to anti-Semitism in France and The European Jewish Congress has demanded action, claiming Anelka should be subjected to the same punishment handed out to those who perform a Nazi salute.
French minister for sport Valerie Fourneyron also condemned the gesture as "shocking" and "disgusting".
But Anelka is adamant it was nothing more than a "special dedication to his friend Dieudonne".
Nicolas Anelka (on Twitter): "I do not know what religion has to do with this story.
"This gesture is a dedication to Dieudonne. With regard to the ministers who give their own interpretations of my quenelle, they are the ones that create confusion and controversy without knowing what the gesture really means.
"I ask people not to be duped by the media.
"And of course I am neither racist nor anti-Semitic."
Dr Moshe Kantor, president of The European Jewish Congress: "It is sickening that such a well-known footballer would make such an abusive and hateful gesture in front of tens of thousands of spectators.
"There should be no room for such intolerance and racism in sports and we expect that the English Premier League officials as well as the police will give Anelka the appropriate punishment.
"We know that English football officials have a very low tolerance for racism at football matches and we hope that all concerned will abhor and show zero-tolerance for this hateful Nazi salute."
"The 'quenelle' is merely a lesser known Nazi salute.
"Furthermore, we hope that this gesture is banned in all places of Europe where Nazi salutes are banned.
"Merely inverting the traditional Nazi salute should not allow anti-Semites to spread and display their hate with impunity."