Frenchman Anelka, 34, celebrated his first of two goals in the 3-3 draw by apparently making a gesture known as the ‘quenelle’ in France, where it can have anti-Semitic connotations. It is made by touching the right shoulder with the left hand, keeping the right arm pointed downwards.
The FA is to investigate the gesture and Anelka could face punishment as severe as a potential 10-match suspension if his actions can be shown to be offensive, insulting, abusive or political.
On Sunday the striker stood by the gesture and insisted it had nothing to do with religion.
"The meaning of 'quenelle' is anti-system. I don't know what it has to do with religion," Anelka said on his Twitter account.
The signal, popularised by French comedian Dieudonne M’bala M’bala, has been described as a reverse Nazi salute and is widely seen as being anti-Zionist and anti-Israeli. Dieudonne claims it is an anti-establishment and not aimed at Jews.
However, France's minister for sport, Valerie Fourneyron has described it as "disgusting" while France's interior minister, Manuel Valls, is considering whether to ban all public appearances by Dieudonne, who has been fined a number of times for hate speech.
"Anelka's gesture is a shocking, disgusting provocation," said Fourneyron. "There is no place for antisemitism and incitement to hatred on the football pitch."
Anelka said on Sunday: "This 'quenelle' was a sign for Dieudonne. As for the ministers who give their own views about my 'quenelle', they are the ones who confuse with something else and stir the controversy without knowing what the gesture really means.
"So I would ask people not to be deceived by the medias. And of course, I'm not anti-semitic nor racist and I take full responsibility for my gesture," he said.
Anelka also published a photo of United States president Barack Obama making a similar - though emphatically not the same - gesture alongside American music stars Jay-Z and Beyonce Knowles.
Journalists in France have widely condemned the act while French Minister of the Interior Manuel Valls told Le Parisien he "will do anything to prevent Dieudonne from campaigning for anti-Semitism and racism", also calling the ‘quenelle’ an anti-Jewish gesture.
West Brom's caretaker coach Keith Downing said both he and Anelka were surprised by the controversy, and said the striker was merely showing support to a friend.
"I'm aware of it, but it has got nothing to do what is being said," Downing told a press conference when asked about the gesture.
"It is dedicated to a French comedian he knows very, very well. He uses it in his act and I think speculation can be stopped now. It is absolute rubbish really.
"He is totally unaware of what the problems were or the speculation that has been thrown around. He is totally surprised by it."
Dieudonne – who originally started out as a left-wing activist but has since aligned himself with far-right parties associated with France’s Front National, and some Islamist organisations – has been convicted for making anti-Semitic remarks on six occasions, and in 2008 was fined 7,000 euros for describing Holocaust remembrance as "memorial pornography".
Anelka has previously been pictured making the gesture with the comedian.
Anelka tweeted to defend the celebration, claiming that it was in support of "my comedian friend Dieudone".
In a series of tweets, French journalist Philippe Auclair described the 'quenelle' as "supposedly an anti-establishment statement but it can also be read as an inversion of the Nazi salute... cretinous at best."
It is not the first time a footballer has celebrated with the ‘quenelle’, a word that can be literally translated a type of savoury dumpling.
Earlier in 2013 Montpellier full-back Mathieu Deplagne celebrated a goal against Sochaux by putting his hand to his opposite shoulder.
The gesture was not widely known at the time and Deplagne was not punished.