Piara Powar, the executive director of the Football Against Racism in Europe (FARE) anti-discrimination network, said Anelka's salute had highlighted the growing influence of far-right groups in football.
The West Brom striker's gesture after scoring against West Ham on Saturday is under investigation by the Football Association. The 'quenelle' - which translates literally as 'dumpling' in English - was brought to prominence by French comedian Dieudonne M'Bala M'Bala, who has been prosecuted for anti-Semitism.
Powar said: "The rise of the far right is one of the most dangerous phenomena facing Europe right now. Whether these are groups of anti-Semites like Dieudonne M'Bala M'Bala, Islamophobic groups like the EDL (English Defence League) or the more usual white power street skinheads, they are active and alive in football.
"In that context alone it was disappointing to see someone like Anelka make the quenelle gesture.
"The English FA now has rules against acts by players of this kind and Anelka will no doubt be punished.
"The gesture made by Anelka is damaging but in my view it is not the same as the abuse meted out by Luis Suarez and John Terry. The context and intent is an important distinguisher."
Both Liverpool striker Suarez and Chelsea defender Terry were banned in 2012 for racially abusing opponents - for eight and four matches respectively,
The quenelle is claimed by some to be an inverted Nazi salute and to have anti-Semitic connotations, and Anelka has promised not to repeat the goal celebration.
Montpellier defender Mathieu Deplagne, Manchester City's Samir Nasri, Liverpool's Mamadou Sakho and NBA basketball star Tony Parker have all been pictured making the salute, but all deny any anti-Semitic connotations.
Powar warned however that it was still "dangerous".
He added: "The fact that the players may have been conned into mimicking something in support of a friend makes it no less a dangerous gesture.
"There is a wider and important context of the rise of someone like Dieudonne M'Bala M'Bala. French race politics and the way in which race plays an increasing part of life in France, are becoming distorted and murky. Many believe that the French integrationist approach to racial diversity is failing.
"No doubt part of the appeal of something like the quenelle is that it has also come to be seen as anti- establishment."
Arsenal manager Arsene Wenger, who first brought Anelka to English football, believes only the player himself can say whether he knew the full implications of his celebration.
Wenger said the meaning of the gesture was not widely known even in France but that players should refrain from celebrating in any way which might "encourage hate".
Wenger told a news conference: "Personally I believe there is only one beautiful way to celebrate a goal and that is to share it with your partners. That should be for me the only way.
"The second thing is that nobody knows in France what it means. Some make it an anti-system movement, some make it an anti-Semitic movement. I think personally I don't know, I have never seen this movement.
"Do we make too much of it? Yes, because he is not (going) to do it again, he has said he will not do it again. Only he can answer whether he knows what it means or not."
Anelka has stated on Twitter it was nothing more than a "special dedication to his friend Dieudonne" but West Brom have conceded the gesture caused offence and he has agreed not to repeat it.
Wenger said if it was proved to be a "lack of respect" then Anelka could expect an FA charge.
He added: "If it is an offence and is recognised as an offence and a lack of respect, you want it to be punished, like every single thing.
"What is important is we respect each other and do not show (lack of respect), especially the sportsmen, who are very popular and watched all over the world. We do not want to encourage hate, we want to encourage understanding and respect."