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."
- Politics & Government
- Crime & Justice