Simon Foster said racist abuse directed at black England players after the Euro 2020 final was "an absolute disgrace" and called for action against those responsible.
And the West Midlands Police and Crime Commissioner said social media platforms that refuse to "do what it takes" to tackle racism and hate should be hauled before the courts.
It comes after ministers launched an investigation into the abuse as part of a clampdown against online racism.
England players Marcus Rashford, Jadon Sancho and Bukayo Saka all received racist abuse on social media after missing penalties in the Euro 2020 final against Italy at Wembley.
Mr Foster said: "The racism and hate that has been directed towards our black England players has been an absolute disgrace.
"I stand in solidarity with the entire England team and in particular with those black players that have been subjected to racism and hate. I trust that those responsible will be held to account via the criminal justice system.
"We need a government that is prepared to demonstrate that same courage, determination and resilience shown by our England team when it comes to doing what it takes to tackle racism and hate in football and wider society.
"When it comes to social media platforms, we need a regulatory regime that is fit for purpose and criminal sanctions for those who run social media platforms, but have not been prepared to do what it takes to tackle racism and hate."
Lichfield MP Michael Fabricant has urged ministers to probe the origins of the online attacks, following claims that the majority of them originated from account holders from abroad.
Responding to his written parliamentary question on the issue, Policing Minister Kit Malthouse, said: "While companies have taken some positive steps, more needs to be done to tackle online harms, including hate crime.
"The upcoming Online Safety regulatory framework will put in place measures to tackle illegal and legal but harmful abuse, including racist abuse.
"If major platforms do not meet their own standards to keep people safe and address abuse quickly and effectively, they could face enforcement action.
"There is no reason for companies to wait until the regime is fully running to take action against this abhorrent abuse, and we will continue to press them to do so.
"The police are reviewing offending material and will work with the relevant social media companies to identify account holders and progress their investigations."