The Professional Footballers' Association says it is "unacceptable" that racist abuse of the kind received by Ian Wright was not prevented.
Former Arsenal and England star Wright on Monday showed a screenshot of racist taunts and death threats he said he was sent by a user on Instagram.
"I know I'm not meant to look at them but these messages still hit me so hard man. This is a child!!!" he wrote.
"This kid as [sic] a direct line into me & is able to send this without any worry."
Ex-Aston Villa striker Gabriel Agbonlahor also received a racist message on Instagram, leading anti-discrimination body Kick It Out to say it was "appalled".
"Racial hate speech and violent threats are totally unacceptable but have become sadly normalised on social media," it said in a statement.
"Whilst we continue to collaborate with social media platforms to ensure a safer user experience for all, these cases should be investigated by law enforcement and the abusers should face criminal sanctions."
The PFA responded to Wright's post by calling on social networks to take greater action against abuse.
"We are disgusted to see the racist abuse aimed at Ian Wright and Gabriel Agbonlahor and their families today. At any time, this is abhorrent behaviour, but when people should be coming together more than ever, it is particularly disturbing," it said.
"It is unacceptable for social networks to allow instances like this to go on. With the technology and expertise at their disposal, there simply must be a way to prevent abuse like this from being sent. Anything less than that is not good enough."