Video footage appeared to show a Manchester City supporter in the home crowd at the Etihad abusing Fred as he prepared to take a corner during the second half.
Fred was also struck by a lighter thrown from the crowd during the incident and it is understood more than one United player was subjected to abuse of a racist nature.
City are working with Greater Manchester Police to identify those responsible and have promised to ban any individual found guilty of racial abuse.
Speaking to ESPN Brazil, Fred said: “Unfortunately, we are still in a backward society. [It is a shame] we still have to live with that in 2019.
“On the field, I didn’t see anything. I saw it only in the locker room afterwards. The guys showed me. He even threw a lighter and it hit me.
“I try not to care about that. I try to look ahead. Unfortunately, this is happening in some stadiums.
“It happened here, it happened in Ukraine with some friends. It’s sad, but we have to keep our heads up and forget about that.”
The Brazilian, who was excellent as United ran out surprise 2-1 winners, added: “We can’t give them any attention because that’s all they want.
“I spoke to the referee after the match, they will do something about it and that’s all.
“We are all the same regardless of skin color, hair and gender. We came from the same place and we all go to the same place when it’s all said and done.
“Thank God I have a lot of friends here in the locker room who hugged me, like [Jesse] Lingard. I don’t want to think about it. I just want to move on.”