The Football Association has been urged to double its minimum ban for racist offences from five matches to 10 following the Nicolas Anelka ruling.
It has been confirmed that neither Anelka nor the FA will appeal against the five-match ban imposed by an independent regulatory commission for the player making an gesture associated with anti-Semitism.
Football's anti-racism organisation Kick It Out claimed it was "beyond feasibility" that Anelka did not know the 'quenelle' salute had anti-Semitic connotations and said people would be perplexed the FA is not appealing against the leniency of the sentence.
It also called on the FA to bring its minimum punishment into line with UEFA's 10-game ban even though the governing body only brought in its five-match rule last year.
Anelka had told the commission he made the gesture as a goal celebration against West Ham on December 28 in support of the French comedian Dieudonne M'bala M'bala, who has been convicted seven times of anti-Semitic crimes, but that he was unaware of any anti-Semitic associations.
A statement from the group read: "Kick It Out finds it difficult to reconcile the sanctions imposed and conclusions reached by the commission.
"There are many ambiguities that are not easily reconcilable with the final outcome. For instance, Anelka has attended one of Dieudonne's live performances and admits to being a friend of his, and to claim that he does not understand the anti-Semitic connotations of the quenelle is beyond feasibility.
"Kick It Out urges the FA to review its anti-discrimination regulations and increase its minimum ban for players found guilty of discriminatory acts to 10 matches, in line with UEFA, so as to provide a much more meaningful deterrent to deal with potential offences."
West Brom have also come in for criticism from Kick It Out.
The statement added: "His employer West Bromwich Albion should have exercised its leadership as a community institution to apologise for the offence caused and deal with the matter in accordance with its disciplinary procedures."
The FA's director of governance Darren Bailey explained why no appeal would be launched.
Bailey said: "We do not consider there is a real prospect of successfully appealing to extend the sanction imposed.
"The grounds of appeal available to us are limited to legal challenges or to circumstances in which the sanction imposed is 'so unduly lenient as to be unreasonable'. That is a high test."
Bailey confirmed the FA had pressed the commission to impose a harsher sanction than five matches.
Anelka will be suspended for the trips to Swansea, Hull and Norwich as well as the home games against Cardiff and Tottenham.