Newcastle United say they "strongly condemn racist abuse" sent to midfielders Bruno Guimaraes and Joe Willock after the win over Arsenal.
Both received messages on social media following Saturday's 1-0 Premier League victory at St James' Park.
Brazil international Guimaraes escaped punishment for appearing to elbow Jorginho in first-half stoppage time.
"Our message is clear. There is no room for racism in football or society," read a Newcastle statement.
"We are providing support to Bruno and Joe and will work with relevant authorities and social media platforms to identify those responsible so that they can be held to account."
English midfielder Willock, who joined Newcastle from Arsenal in 2021 after a loan spell, provided the cross which led to Anthony Gordon's controversial 64th-minute winner.
Defeat was Arsenal's first in the league season.
Arsenal said they take a "zero tolerance approach" to all forms of discrimination and "will apply the strongest possible action to anyone we can identify sending hateful messages".
The Premier League said it "condemns any form of discriminatory abuse and actively works with all players, clubs, platforms, and authorities to help bring offenders of hate crime to justice".
Anti-discrimination charity Kick it Out said it wants the government's new Online Safety Bill to help prevent such abuse.
"Sadly, this has been an almost weekly occurrence this season, and the costs on players' mental health are huge," it said.
"Social media companies cannot continue to allow this to happen without consequence, but they can offer better safeguards right now."