Footage appeared to show a Man City supporter making a monkey gesture and shouting “black b*****d" as the Brazilian and Jesse Lingard strode over to a take a corner during United's 2-1 win at The Etihad on Saturday.
The 26-year-old was then pelted with missiles as a bottle of water and several lighters were hurled from the stands, with one object striking the midfielder on the back.
Speaking to ESPN afterwards, 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."
He added: “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.
“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 colour, 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 Lingard. I don't want to think about it. I just want to move on."