Saka, 19, had not long been on the pitch when the game went to a penalty shootout with the score at 1-1.
Within minutes of his shot being saved, he received abuse on his Instagram account, which was flooded with monkey emojis.
Other fans rallied to support the teenager, promising to get the offensive comments reported and removed.
The FA said it was “appalled by the online racism” aimed at some players on social media.
“We could not be clearer that anyone behind such disgusting behaviour is not welcome in following the team,” a spokesperson said. “We will do all we can to support the players affected while urging the toughest punishments possible for anyone responsible.
“We will continue to do everything we can to stamp discrimination out of the game, but we implore government to act quickly and bring in the appropriate legislation so this abuse has real life consequences.
“Social media companies need to step up and take accountability and action to ban abusers from their platforms, gather evidence that can lead to prosecution and support making their platforms free from this type of abhorrent abuse.”