The West Brom striker caused uproar with his gesture, which is claimed by some to be an inverted Nazi salute and to have anti-Semitic connotations. The Football Association is currently investigating.
Wenger, the Arsenal manager who first brought Anelka to English football, said the meaning of the gesture was not widely known even in France.
The Gunners boss does believe however 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 knew what it meant or not."
The 'quenelle' salute was brought to prominence in France by comedian Dieudonne M'Bala M'Bala, who has been prosecuted for anti-Semitism.
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."
Pictures have also emerged of two other French players, Samir Nasri and Mamadou Sakho, performing the gesture.
Nasri clarified his position, stressing it was his view that it should be portrayed as an anti-establishment gesture rather than anything more sinister.
He said on Twitter: "The pose in the picture i posted over 2 months ago symbolises being against the system. Its has absolutely nothing to do with being anti semitic or against jewish people. I apologise for causing any hurt to anyone who might have been mislead into thinking this means anything of that nature."
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."