The Uruguayan striker served an eight-match ban as a result of using a racially derogatory term towards the Frenchman, but Liverpool have been reluctant to accept that their player is guilty and Suarez himself is yet to apologise directly to Evra.
In an open letter to the club and manager Kenny Dalglish, who has been criticised for his handling of the episode, the group have asked for the Reds to acknowledge the Football Association’s findings.
Head of the group, Gloria Hyatt, insists Liverpool have been reckless in their treatment of the incident and believes their attitude does not reflect that of the people in the city who work to counter racism.
She told reporters: "Liverpool FC has presided over the worst incident of racism in football seen in recent years.
"Their misguided handling of the saga has let down all of those in the city who work hard to challenge racism and to make Liverpool a better place to live for everyone."
Activist Lee Jasper, a former equality aide London Mayor Ken Livingston, claims Liverpool has failed the city and the nation with their lack of leadership over the issue..
Jasper said: "The club, including the owners, the players and the manager need to realise the enormous damage caused by their reluctance and obdurate behaviour.
"Kenny Dalglish used to manage Celtic. He ought to know the importance of stamping out bigotry.
“The club failed the city, the nation as a whole, and Britain's black communities. Their abysmal lack of leadership on these issues has given a green light to racism.
"They must make urgent reparations and a clear and unequivocal apology."