The claim was made by Peter Herbert, chairman of the Society of Black Lawyers (SBL), who also criticised European champions Chelsea after police dropped an investigation into referee Mark Clattenburg.
The FA enquiry into the incident is continuing.
Chelsea complained to the FA that the referee used a term understood to have been interpreted as racist towards Nigeria's John Obi Mikel during the 3-2 Premier League defeat by Manchester United at Stamford Bridge on October 28.
Although the club did not take the matter to the police, the SBL did lodge a complaint with London's Metropolitan force.
But the police said Tuesday they were taking no further action "because no victims had come forward".
That prompted Herbert to slam the FA and Chelsea for failing to report the allegations to the police.
But Bernstein said: "These ill-informed and unhelpful remarks are at odds with the progressive and responsible approach being followed by the game with the support of (the British) government to deal with these serious issues.
"The FA will continue working to strengthen processes to eradicate all forms of discrimination in football."
Herbert alleged there was "a cosy little agreement between Chelsea FC and the FA not to report these matters to the Metropolitan Police but to have them dealt with solely by the FA".
He also told Sky Sports News the FA were "institutionally racist" -- a charged term in Britain, stemming from a 1999 report into the Metropolitan Police's handling of an investigation into the murder of black teenager Stephen Lawrence.
"Institutionally racist? Of course it is," Herbert said of the FA.
"They don't even implement what the Stephen Lawrence inquiry recommendations were about how to report a racial incident, whether the victim or any other person believes it is.
"If an institution fails to follow 14 years after the MacPherson Report's recommendations and it has a history of under-reporting race hate, what would you call it? We would call it institutionally racist."
However, Clarke Carlisle, the black chairman of England's Professional Footballers Association, defended Chelsea and the FA.
"I think it would have been better if it remained within the remit of Chelsea and the FA to put any subsequent case to the Met Police," Carlisle said.
"If we reported all incidents from third-party evidence, there would be many investigations the police would have to go through.
"We have to have faith Chelsea have reported the incidents in good faith and that the FA will deal with it accordingly, and report it to the police if necessary."