Twitter has said it will not end the practice of allowing people to post from anonymous accounts.
Arsenal chief executive Vinai Venkatesham on Thursday described abuse to black players on various social media sites as the "biggest problem" in football, and said its impact "cannot be underestimated".
On Friday, Gunners winger Willian called for change after sharing screenshots of abuse sent to him by two different Instagram users following Arsenal's 1-1 Europa League draw against Benfica.
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The Brazilian's Arsenal team-mate Eddie Nketiah, Manchester United's Marcus Rashford, Anthony Martial and Lauren James and Chelsea full-back Reece James - Lauren's brother - are among the other footballers to have recently suffered racist abuse on social media.
A number of the abusive messages have come from accounts where an individual hides behind a pseudonym, and it has been repeatedly mentioned within football that social media companies should prevent anonymous users.
But defending its policy, Twitter said: "At Twitter, we are guided by our values, and never more so than when it comes to fundamental issues like identity.
"We believe everyone has the right to share their voice without requiring a government ID to do so.
"Pseudonymity has been a vital tool for speaking out in oppressive regimes, it is no less critical in democratic societies. Pseudonymity may be used to explore your identity, to find support as victims of crimes, or to highlight issues faced by vulnerable communities.
"Indeed, many of the first voices to speak out on societal wrongdoings, have done so behind some degree of pseudonymity - once they do, their experience can encourage others to do the same, knowing they don't have to put their name to their experience if they're not comfortable doing so.
"Perhaps most fundamentally of all - some of the communities who may lack access to government IDs are exactly those who we strive to give a voice to on Twitter."
Willian shared screenshots of abusive messages on his Instagram Story on Friday and added the caption: "Something needs to change! The fight against racism continues."
Arsenal team-mate Nketiah posted on his Twitter account that it was "time for change" - a message supported by the official England account, which said: "We are with you, Eddie Nketiah. This has to stop."
Twitter said there have been over 11m tweets about football in the UK since September, of which more than 5,000 have been removed for violating the social network's rules.
The American company vowed to continue improvements on its own in-house technology, while working alongside the UK Government and football authorities, including anti-racism group Kick It Out.
In the statement, Twitter continued: "We are acutely aware that many high-profile users can, at times, be particularly vulnerable to abuse and harassment.
"As long as any one person is targeted with abusive behaviour on our service, our work will not be done.
"We will continue to challenge this abhorrent behaviour at source along with our football partners and other social media companies.
"We join our partners in condemning racism and we will continue to play our part in tackling this unacceptable behaviour - both online and offline. We want to reiterate - there is no room for racist abuse on Twitter."
'Clubs have duty of care to players in fight against racism'
Brighton chief executive Paul Barber insists football clubs have a duty of care to their players in the fight against discrimination, but believes social media companies must do more to help that support on offer.
Social media companies have been under pressure to inflict harsher punishments on accounts that violate their rules, especially discrimination, and Barber added his voice to that calls for more help from such companies, as his club does its best to look after their employees.
"We are employers, and we have a duty of care to our staff, and those staff include our players," Barber told Sky Sports. "Players should not have to worry about being discriminated against just because they are footballers.
"They have the same rights as every other employee in the country and they have a right to go out and do their jobs and not suffer the kind of hate we have seen in recent weeks and months.
"Clubs can take their own actions but we need some help from the social media companies to take some responsibility for their own sites and what goes on to them and when complaints are made to get various derogatory comments taken down, they are as quickly as possible."
Much of the abuse directed at footballers comes via platforms such as Twitter and Instagram, but Barber revealed club channels on social media and their own website are also used by abusers.
"Just this week alone we have had hundreds of posts on our own channels that have had to have been removed because they are discriminatory, abusive or in some way derogatory towards individuals," he added. "We have had to ban individuals from those sites because they have been persistent with the abuse that they are trying to push out.
"We are now hoping that people are realising that this is unacceptable and our zero-tolerance approach will lead to sanctions within the stadium if we can then identify those individuals."
Kick It Out reporting racism
Kick It Out is football's equality and inclusion organisation - working throughout the football, educational and community sectors to challenge discrimination, encourage inclusive practices, and campaign for positive change.
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