Everton condemned supporters for targeting a Chelsea player with homophobic chants during Thursday's 1-1 Premier League draw at Stamford Bridge.
"Such behaviour is unacceptable and does not represent the values of our club or our wider fanbase," the Merseyside club said in a statement.
"We promote and celebrate the diversity and inclusivity within our club, our game and our community. We expect fans to reflect those values by refraining from any discriminatory chanting in the future."
In August, Liverpool condemned fans for homophobic chants aimed at Scotland midfielder Billy Gilmour, who is on loan at Norwich City from Chelsea.