Pogba won the penalty himself and after consulting with Marcus Rashford, who scored from the spot against Chelsea in their opening Premier League game, saw his effort saved by Rui Patricio.
The former Juventus midfielder is the third footballer in England to suffer online racist abuse in just over a week following penalty misses.
Chelsea striker Tammy Abraham suffered similar vilification after missing a penalty in the UEFA Super Cup against Liverpool last Wednesday while Reading forward Yakou Meite shared screenshots of racist messages he received after missing from the spot against Cardiff on Sunday.
United released a statement early Tuesday morning condemning the abuse on Pogba and indicated they were working tirelessly to identify the culprits and punish them accordingly.
It read: "Everyone at Manchester United is disgusted by the racial abuse aimed at Paul Pogba last night and we utterly condemn it.
"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.
"Manchester United has zero tolerance of any form of racism or discrimination and a long-standing commitment to campaigning against it through our #AllRedAllEqual initiative.
"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."