The Frenchman was subjected to abuse after missing a penalty in Manchester United's 1-1 draw with Wolves on Monday, with Twitter having since confirmed that it will meet United and anti-racism pressure group Kick It Out to discuss a solution to the ongoing problem.
Solskjaer says that the abuse only makes Pogba stronger but says that something must be done to ensure that no further players are subjected to such treatment.
“Paul is fine, he’s a strong character and it makes him stronger," he told reporters.
"I cannot believe we still sit here in 2019 taking about these instances.
“Social media is a place where people can hide behind fake identities. There’s so many Ole Gunnar Solskjaers on social media that I know are not me.
“The authorities have got to do something about the ones who spread this hate. You feel sorry for them really – they must have problems themselves.”
Chelsea's Tammy Abraham and Reading's Yakou Meite have also been subjected to racist abuse in August after missing penalties.