West Brom conceded the gesture had caused offence and have asked Anelka not to repeat the celebration, which is still being investigated by the FA.
The French striker has denied the salute had any anti-Semitic connotations but he caused a storm in his native France by the gesture during the 3-3 draw with West Ham.
West Brom caretaker boss Keith Downing said Anelka had been taken aback by the fury his actions had generated.
Downing said: "He was kind of surprised by the reaction that's happened but we've stated already it won't happen again. The reaction from it was obviously not favourable."
Downing said he may pick the striker for the match against Newcastle on Wednesday but admitted that the controversy - which is still being investigated by the FA - has become a distraction.
A statement issued by West Brom said: "The club fully acknowledges that Nicolas' goal celebration has caused offence in some quarters and has asked Nicolas not to perform the gesture again. Nicolas immediately agreed to adhere to this request."
The 'quenelle' salute was brought to prominence in his homeland by French comedian Dieudonne M'Bala M'Bala, who has been prosecuted for anti-Semitism. The European Jewish Congress has demanded action against Anelka, claiming it is an inverted Nazi salute.
French minister for sport Valerie Fourneyron also condemned the gesture as "shocking" and "disgusting".
Anelka has stated on Twitter it was nothing more than a "special dedication to [his] friend Dieudonne".
The West Brom statement said the club's own investigation was continuing alongside the FA's.
It added: "Nicolas said that he performed the gesture to dedicate his goal to a friend and vehemently denied having any intention to cause offence.
"Upon reporting for training this morning, Nicolas was asked by sporting and technical director Richard Garlick to give a full explanation about his goal celebration, during which he again strongly denied intending to cause offence."
Pictures have also emerged of two other French players, Samir Nasri and Mamadou Sakho, performing the gesture.
The photograph of Manchester City playmaker Nasri was taken outside the club's Carrington training base and is thought to date back to November.
It is understood that Nasri was unaware of the anti-Semitic or political connotations of the gesture.
Liverpool defender Sakho said in November that he was tricked into performing the gesture.
He wrote on his Twitter account: "This photo was taken six months ago, I did not know the meaning of this gesture, I got trapped!"
On Monday, a Liverpool spokesperson told Press Association Sport: "Mamadou Sakho has explained that when posing for the photo, taken over six months ago, he had no knowledge of any meaning or significance attached to the gesture."