The claim was made by Peter Herbert, chair of the Society of Black Lawyers, who also criticised the FA and Chelsea after the police dropped an investigation into referee Mark Clattenburg.
Bernstein said in a statement: "These ill-informed and unhelpful remarks are at odds with the progressive and responsible approach being followed by the game with the support of Government to deal with these serious issues.
"The FA will continue working to strengthen processes to eradicate all forms of discrimination in football."
Herbert hit out at the FA and Chelsea for not reporting allegations that top-flight referee Clattenburg used comments understood to have been interpreted as racist to the police.
The FA are investigating the matter after receiving a complaint from the club but neither body involved police.
The SBL did make a complaint to the Metropolitan Police based on media reports of the alleged incident but officials at Scotland Yard have announced no action will be taken "because no victims had come forward".
Herbert said in a statement: "It would appear that there is 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.
"The FA have a dreadful record of indifference on hate crime generally; failing to challenge anti-Semitism at Tottenham Hotspur and at other grounds; eventually finding John Terry made a racist remark but remarkably found him not to be a 'racist'; whilst the derisory penalty of a four or eight-match ban [Luis Suarez] is believed to be a suitable punishment for what in any other industry would be summary dismissal for gross misconduct."
Herbert also claimed on Sky Sports News the FA were "institutionally racist".
He added: "Institutionally racist? Of course it is. They don't even implement what the Stephen Lawrence inquiry (MacPherson Report) recommendations were about how to report a racial incident, whether the victim or any other person believes it is.
"You will not find that on the FA website or any of the training given to referees, managers, coaches or players. It isn't there. It should be.
"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."
Professional Footballers' Association chairman Clarke Carlisle defended Chelsea and the FA.
Carlisle, speaking at the Street League Academy in Manchester, said: "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.
"It is an allegation they are currently investigating themselves.
"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."
Clattenburg is alleged to have used a term which could be interpreted as racist to Chelsea midfielder John Obi Mikel during the Barclays Premier League game against Manchester United at Stamford Bridge on October 28.
The FA is expected to announce the outcome of its investigation into Chelsea's complaint within 48 hours.
It is understood Chelsea acted in the belief that the FA was the appropriate organisation to deal with their complaint rather than the police.
Herbert said he would raise his views with the sports minister Hugh Robertson.
The minister however said he could not issue orders to Chelsea to involve the police.
Robertson told the Press Association: "They are welcome to approach me but I cannot instruct Chelsea to make criminal complaints, that is an argument he needs to have with Chelsea.
He added: "We had the Downing Street summit [on racism in football] earlier in the year and the FA are coming back to us before the end of the year and as soon as we have that response we will assess what to do next."