The France World Cup winner was racially abused on social media after his penalty miss at Wolves on Monday.
Several of Pogba’s team-mates criticised the abuse, while England women’s manager Phil Neville called for footballers to “boycott” social media.
“Racist insults are ignorance,” said 26-year-old Pogba.
In a message on Twitter, accompanied by a photograph showing him holding his baby alongside portraits of his late father Fassou Antoine and civil rights activist Martin Luther King, he added: “My ancestors and my parents suffered for my generation to be free today, to work, to take the bus, to play football.”
It was the first time Pogba had tweeted since July.
On Saturday, United manager Ole Gunnar Solskjaer said people who post racist abuse on social media “hide behind fake identities”.
It’s the fourth racism incident in two weeks – Chelsea striker Tammy Abraham and Reading’s Yakou Meite both received racist messages online after missing penalties in their teams’ most recent matches.
Twitter said it will meet any stakeholders to show the “proactive work” being done to tackle abuse.