England women's manager Phil Neville said footballers should "boycott" social media to send a "powerful message" that abuse is not acceptable.
"We have to take drastic measures now as a football community. I've had it with my players on social media, the Premier League and the Championship have had it," said Neville.
"I just wonder whether as a football community we come off social media, because Twitter won't do anything about it, Instagram won't do anything about it - they send you an email reply saying they'll investigate but nothing happens.
"I've lost total faith in whoever runs these social media departments, so let's send a powerful message: come off social media (for) six months. Let's see the effect it has on these social media companies."
On Tuesday, Twitter issued a statement saying it "strongly condemns" the abuse and has "now permanently suspended a series of accounts for violating our hateful conduct policy".
It added: "We're fully aware of and share the concerns surrounding online racist abuse towards certain footballers in the UK over recent days.
"We're proactively monitoring the conversation online and will continue taking robust action on any account which violates our rules.
"This is a societal issue and requires a societal response. This is why we maintain a dialogue with both the Professional Footballers' Association and Kick It Out and are committed to working together to address abusive online and racist behaviour across the industry."
A statement from Facebook said: "There is no place for racism or abusive behaviour on Instagram and we invest heavily in developing tools and technologies to prevent bullying and harassment.
"People who repeatedly break our guidelines will be permanently banned from using Instagram."
Several of Pogba's team-mates have criticised the abuse of the Frenchman, whose 68th-minute penalty was saved by Wolves goalkeeper Rui Patricio - the fourth spot-kick Pogba has missed for United in the Premier League since the start of last season.
Harry Maguire called on social media companies to "stop these pathetic trolls", while Marcus Rashford said "enough now, this needs to stop".
"Manchester United is a family. Paul Pogba is a huge part of that family. You attack him you attack us all," the England striker added on Twitter.
United said they are "working to identify" those responsible for the racist abuse directed at Pogba.
"The individuals who expressed these views do not represent the values of our great club and it is encouraging to see the vast majority of our fans condemn this on social media also," read a United statement.
"We will work to identify the few involved in these incidents and take the strongest course of action available to us. We also encourage social media companies to take action in these cases."