Sterling was also pelted with cups after scoring England’s opening goal on Thursday night.
Prime Minister Boris Johnson called on FIFA to act, and world football’s governing body has pledged to do so.
"First and foremost, FIFA strongly rejects any form of racism and violence and has a very clear zero tolerance stance for such behaviour in football," a statement from the governing body read.
"FIFA will take adequate actions as soon as it receives match reports concerning yesterday’s Hungary-England game.
"With regards to the previous UEFA sanction against Hungary, please note that as specified by UEFA at the time, this sanction is to be served in UEFA competitions.”
A UEFA statement said: “UEFA strongly condemns any discriminatory/racist behaviour and we will continue to lead the fight against racism and discrimination in the game.
“The alleged incidents happened in a FIFA competition and do therefore not fall under the jurisdiction of our disciplinary bodies.”