Kick It Out's Lord Ouseley has labelled Liverpool "hypocritical" over their handling of Luis Suarez's eight-match ban for racially abusing Patrice Evra.
Liverpool players wore T-shirts in support of Uruguayan Suarez - a move Ouseley has called "dreadful".
Lord Ouseley also said Reds striker Suarez's apology was "lamentable".
The anti-racism campaign's chairman said: "Liverpool need to take a hard look at themselves. Suarez's attempt at a belated apology is lamentable."
Liverpool are not appealing against the Football Association suspension and £40,000 fine imposed on Suarez by an independent commission for his comments towards Manchester United defender Evra at Anfield on 15 October.
Suarez did not mention Evra by name in his apology and has also stated that he would carry out the suspension "with the resignation of someone who hasn't done anything wrong".
Kick It Out had previously commended Liverpool for choosing not to appeal against the ban.
A statement on its website on Wednesday said: "We commend Liverpool FC in bringing closure to this matter, reaffirming its commitment to an unequivocal, zero-tolerance approach towards discrimination in football."
However, Lord Ouseley, who was chairman of the Commission for Racial Equality from 1993 to 2000, wrote in the Guardian: "Liverpool need to take a hard look at themselves and how they have responded to the complaint and the investigations into the allegations of abuse in the Patrice Evra/Luis Suarez case.
"Throughout the entirety of the proceedings, over the past three months, all we have heard are denials and denigration of Evra.
"Since the publication of the 115-page report of the findings of the FA's independent commission, Liverpool's vitriol has increased.
"Suarez's attempt at a belated apology is nothing short of lamentable.
"I cannot believe that a club of Liverpool's stature, and with how it has previously led on matters of social injustice and inequality, can allow its integrity and credibility to be debased by such crass and ill-considered responses.
"Liverpool have been particularly hypocritical. You can't on the one hand wear a Kick It Out T-shirt in a week of campaigning against racism when this is also happening on the pitch: it's the height of hypocrisy.
"Liverpool players wore a T-shirt saying: 'We support Luis Suarez', seemingly whatever the outcome. This was a dreadful knee-jerk reaction because it stirs things up."
Piara Powar, executive director of Football Against Racism in Europe, believes the FA would be within its rights to charge Liverpool and its manager Kenny Dalglish over their handling of the situation.
"Liverpool have constantly undermined the investigation and its outcome," he told BBC Sport.
"They have been disrespectful to the FA and questioned its integrity and neutrality.
"If a manager had done that in a post-match interview the FA would have brought disrepute charges."
It is understood that the FA has no plans to charge either Liverpool or Dalglish.