The French striker performed the controversial salute after scoring in December's 3-3 draw at West Ham in the Premier League and was charged by the FA in January.
However, the governing body confirmed on Thursday that it would not contest the Independent Regulatory Commission's recommendation of a five-match suspension, with director of football governance and regulation Darren Bailey releasing a statement to explain the FA's stance.
Anelka denied the initial charge and defended the gesture by claiming that it was "anti-system" and a dedication to his friend and comedian Dieudonne M'bala M'bala, as opposed to being anti-Semitic.
"Nicolas Anelka's use of the 'quenelle' was the first time this gesture had been seen in the English game," said Bailey on the FA's official website.
"We acknowledged from the very outset the unusual nature of this incident and the sensitivities surrounding it, and so wanted to ensure we conducted a proper and thorough investigation.
"Whilst some commentators criticized the time we took to build the prosecution case at the beginning, we hope it is now clear why it was essential to take the time we did to issue the charges. The focus had to be on the investigation.
"Despite the pressure to make public comment at that time, it will never be appropriate for a regulatory body to offer a running commentary on its investigation, as this risks undermining the fairness of its process.
"This was a complex case. It required detailed expert consideration of a range of issues: including the nature of the conduct - a gesture as opposed to the spoken word presenting unique challenges; the controversy over its meaning in France; the developing ideology of the gesture's inventor; and the state of mind of its user.
"The FA placed nearly 200 pages of evidence before the Independent Regulatory Commission and two hours of carefully researched video footage, which we translated from the original French and subtitled into English to make it comprehensible to an English tribunal.
"Ultimately, the Independent Regulatory Commission was persuaded to accept The FA's case against Nicolas Anelka. We acknowledge the careful consideration taken by the Independent Regulatory Commission of the difficult arguments placed before it.
"Its decision makes it absolutely clear that use of this gesture on the football pitches of England will not be tolerated in any circumstance.
"Whilst the FA pressed the Independent Regulatory Commission to impose a harsher sanction on Nicolas Anelka than a suspension of five matches, it is not so far outside the range of sanctions that would have been appropriate in this case to be properly described as unreasonable.
"Prior to The FA charging Mr. Anelka, we understand that no other sports regulatory or prosecutorial body in the world had sought to tackle this gesture and the complex ambiguities of its meaning.
"We accept that, even though we are a sports governing body, the extent of public interest in what we do means that we are sometimes required to be in the vanguard of anti-discriminatory and disciplinary action of this type.
"Our response demonstrates that we are prepared to act decisively and expeditiously in addressing these matters head-on."