In a statement, the FA said that “social media companies need to step up and take accountability” and on Monday morning Twitter confirmed a number of accounts had been banned.
“The abhorrent racist abuse last night has absolutely no place on Twitter,” a Twitter spokesperson said.
“In the past 24 hours, through a combination of machine learning based automation and human review, we have swiftly removed over 1,000 Tweets and permanently suspended a number of accounts for violating our rules - the vast majority of which we detected ourselves proactively using technology.
“We will continue to take action when we identify any Tweets or accounts that violate our policies.
“We have proactively engaged and continue to collaborate with our partners across the football community to identify ways to tackle this issue collectively and will continue to play our part in curbing this unacceptable behaviour - both online and offline.”
Facebook - which owns Instagram - said it tries to remove harmful content as quickly as possible and encouraged people to use the tools it offers to block abuse.
“No one should have to experience racist abuse anywhere, and we don’t want it on Instagram,” a Facebook company spokesperson said.
“We quickly removed comments and accounts directing abuse at England’s footballers last night and we’ll continue to take action against those that break our rules.
“In addition to our work to remove this content, we encourage all players to turn on Hidden Words, a tool which means no one has to see abuse in their comments or DMs.
“No one thing will fix this challenge overnight, but we’re committed to keeping our community safe from abuse.”