Anelka was charged on Tuesday for the gesture, which is understood to have anti-Semitic connotations.
Anelka performed the salute after scoring for the Baggies against West Ham on December 28.
However, the 34-year-old has continued to profess his innocence by claiming that it was in support of his friend, the French comedian Dieudonne M'bala M'bala.
Anelka has now questioned the FA's decision to hire an expert for their investigation into the matter.
He believes that the salute would have interpreted correctly if the governing body had instead listened to a leading Jewish voice in France.
"The English football Federation hired an expert to decide the meaning of my 'quenelle'... The latter concluded that my gesture had an anti-Semitic connotation, which led to my indictment by the FA," he wrote on his official Facebook page.
"It would have been legitimate that this expert is french, living in France, and that could have an exact knowledge of my gesture.
"What better expert than Mr. Cukierman, president of CRIF (Conseil Representatif France Jewish Institutions), which explains it very clearly that my 'quenelle' could not be considered to be anti-Semitic! He also explained accurately and at what time this gesture could have such a connotation.
"I therefore ask the English Federation to kindly remove the charge with which I am accused. And I repeat, I am neither anti-Semitic nor racist."
Anelka has until 6pm on Thursday to formally respond to the charge.