The 34-year-old scored his first Baggies goals with a brace at Upton Park after being recalled to the starting line-up for the first time in over two months.
But during his celebration for his first strike, which levelled the game following Joe Cole's effort for the Hammers, Anelka seemingly performed the 'quenelle' salute made famous by French comedian Dieudonne.
The gesture has been linked to anti-Semitism in his homeland.
After West Brom caretaker manager Keith Downing said Anelka had been "surprised" by the resulting outcry, the player on Saturday night claimed the salute had simply been made as a "special dedication" to his friend.
"This gesture was just a special dedication to my comedian friend Dieudonne," he tweeted in both French and English on his official account.
However, the French minister for sport Valerie Fourneyron had earlier condemned the gesture on Twitter, describing it as "shocking" and "disgusting".
She wrote: "Anelka's gesture is a shocking provocation, disgusting. There's no place for anti-Semitism and incitement to hatred on the football field."
Interim Baggies boss Keith Downing was quick to defend Anelka.
"I'm aware of it but it has got nothing to do with what is being said," Downing replied 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."
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