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: “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.”
Herbert also claimed 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.”
Professional Footballers’ Association chairman Clarke Carlisle, now playing at York City, 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,” said Clarke.
“If we reported all incidents from third-party evidence, there would be many investigations the police would have to go through.”