The Professional Footballers' Association has issued a six-point action plan to deal with racism.
Criticised for not doing enough to tackle the problem, the PFA says it is now time for tougher penalties.
Culprits could be sacked and ordered to attend awareness programmes.
The response comes after Reading striker Jason Roberts, a member of the PFA's management committee, expressed frustration that his recommendations had not been acted on.
The PFA's plan calls for:
- Speeding up the process of dealing with reported racist abuse with close monitoring of any incidents
- Consideration of stiffer penalties for racist abuse and to include an equality awareness programme for culprits and clubs involved
- An English form of the "Rooney rule" - introduced by American football's National Football League in 2003 - to make sure qualified ethnic minority coaches are on interview lists for job vacancies
- The proportion of black coaches and managers to be monitored and any inequality or progress highlighted
- Racial abuse to be considered gross misconduct in player and coach contracts (and therefore potentially a sackable offence)
- Not losing sight of other equality issues such as gender, sexual orientation, disability, anti-Semitism, Islamophobia and Asians in football
Some of the proposals would require the intervention of the Football Association or Premier League.
In response, the Premier League said: "We have not yet received this proposal from the PFA and were not aware of it prior to the media coverage [on Wednesday].
"When we receive this proposal we will of course discuss it with the PFA at our regular meetings and engage with other organisations, including our clubs, the FA, Football League and the League Managers' Association to discuss these important issues."
PFA chief Gordon Taylor said football needed a united front in tackling racism and that a breakaway player organisation would detract from this.
He also added that Roberts and other notable former and current players had been involved in consultations with the PFA in drawing up the plan.
"Above all we have black former players, who have become coaches, who are looking for opportunities and see the limited chances they have been given. This is something we are continually working on," Taylor told BBC Radio 5 live.
"Jason is round the table, so is Darren Moore, Clarke Carlisle and other trustees and noted black players and managers such as Garth Crooks, Paul Elliott, Chris Powell and Brendon Batson.
"We need all the football family on this together. Nobody said racism was easy to deal with. We saw what happened in Serbia… but we have to do our best and we need the fire in the belly of a lot of the younger players to be on board with this and making sure they understand the process and are part of it.
"Then they can feel the sense of achievement at the end of the day in line with the progress we have made so far."
On a potential black players' association, Taylor added: "If they want their own particular select group who they feel they can influence everybody more than the whole PFA as a union together, I would say they are seriously mistaken," said Taylor.
"If we are not careful, this will set us back years. It would not only set back the game, it would set back the anti-racist initiative."
His views are echoed by former West Bromwich Albion and Arsenal defender Batson.
Batson, a former PFA administrator, told BBC Radio 5 live: "I don't think there would be any benefit.
"What we need to do is address the concerns of current black players, hear their voice and see if we can do something about it.
"We need to harness the anger of the current players and let it be an instrument for change, but I don't think a split will help the situation."
FA chairman David Bernstein announced on Tuesday that the governing body will review the sanctions for racist abuse following the John Terry case.
The Chelsea defender was banned for four games after being found guilty of abusing Queens Park Rangers defender Anton Ferdinand, a punishment Bernstein felt was "about right".