A national anti-racism organisation wants a summit meeting to tackle the grievances of footballers who boycotted the Kick It Out T-shirt campaign.
Show Racism the Red Card says it understands why players opted not to show their support at the weekend.
Both Rio Ferdinand and Jason Roberts refused to wear the shirts publicising Kick It Out's awareness drive.
The players are believed to be unhappy at Kick It Out's lack of response over recent high-profile racial abuse cases.
A statement from Show Racism the Red Card said it fully understood "the anger of the Ferdinand family and Jason Roberts" in relation to the Football Association's handling of the John Terry case.
But it added that it was now time for players to sit down with Show Racism the Red Card, Kick It Out and the Professional Footballers' Association in order to draw up a plan of action to present to the footballing authorities and government.
Kick It Out's annual fortnight of anti-racism action started on Thursday and runs until 29 October.
Premier League players traditionally wear T-shirts during this time as a show of support for the campaign group and its message.
But several high-profile footballers, including Manchester United defender Ferdinand, his brother Anton, who plays for QPR, and Reading striker Roberts, chose not to wear the T-shirts at the weekend.
Roberts said before his side's game with Liverpool that he did not intend to wear a shirt because he felt that Kick It Out was not being "strong enough".
Recent cases involving Chelsea captain Terry and Liverpool striker Luis Suarez have highlighted the problem of racism in football.
Terry was fined £220,000 for racially abusing Anton Ferdinand, while Liverpool's Suarez was banned for eight matches and given a £40,000 fine for racially abusing Manchester United's Patrice Evra.
Former Fulham and West Ham striker Leroy Rosenior, an ambassador for Show Racism the Red Card, said the decision of some players not to wear the T-shirts was wrong and called on them to do more to help stamp out racism.
"I found it a little silly from the players," he said. "Players need to give up their time and energy to move this thing forward.
"I understand where Rio and Anton are coming from after what their families have been through, but I thought it wasn't constructive in terms of moving the debate forward.
"It hasn't been top of the FA agenda for a long, long time. They have got better but they are not doing enough. But we need the players to be unified and to work with organisations to do better."
Rosenior said Kick It Out cannot do more than it is already doing.
"They haven't got the authority, they haven't got the manpower and they certainly haven't got the funds, so they need players like Jason Roberts to get behind it," he said.
Former England star John Barnes believes football can only eradicate racism once the problem is removed from society.
"You can't target racism in football as long as it exists in society," he told BBC Sport.
"We're trying to do it the wrong way round. A lot can be done but all we can do in football is target and tackle the symptom."
Barnes has sympathy for the stand that was made by Roberts but believes Kick It Out is facing a difficult task.
He added: "Jason has to do what he thinks is right and maybe he thinks it will take something like this for more strong action to be taken.
"I have a lot of empathy but also with Kick It Out, too. We still have a long way to go."
Lord Ouseley, chairman of the Kick It Out group, said he understood the frustrations of players but urged them to speak out if they encountered racism in the game.
"The issue is that the T-shirts have become the story whereas the actual grievances of black players, both current and former, have not come out in the open," he told BBC Radio 5 live.
"We need to be talking about what their legitimate grievances are and how they can be tackled and resolved."