The Football Association has decided it will not appeal against Nicolas Anelka's five-match ban for making the quenelle gesture.
An independent commission handed out the ban - the minimum available - to the player after he performed the gesture in a Premier League game.
The FA had wanted a more severe punishment but has now said it does not think an appeal would succeed.
Darren Bailey, the FA's head of governance and regulation, said: "Having now considered very carefully the written reasons of the Independent Regulatory Commission together with our appointed QC, 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."
The football body went on to say that it pressed for a "harsher sanction" during the commission's tribunal, but described the five match ban as not "unreasonable".
Anti-racism group Kick It Out and Jewish communal organisations including the Board of Deputies and the Community Security Trust earlier this week strongly urged the FA to appeal in favour of a longer ban.
The groups also called the written reasoning provided by the independent commission "baffling", "illogical" and "contradictory".
Anelka, who made the gesture, a Nazi-style salute, during a match in December, had been charged with two breaches of the FA's anti-discrimination rules. He denied the charges, claiming that the gesture was a tribute to his friend, the French comedian Dieudonne M'bala, who has been convicted of antisemitic offences eight times.
The player, who was also fined £80,000 and ordered to attend an education course, has decided not to appeal.
