The Premier League has launched the No Room for Racism campaign as part of its commitment to help tackle discrimination on and off the pitch.
Fulham and Manchester City players wore "Kick it out" t-shirts - including Raheem Sterling, who was playing for England when the players were racially abused in Montenegro on Monday.
The campaign runs until Monday April 8, sending a clear message that racism is not acceptable in the Premier League or the wider sport.
Some Fulham fans said they would like to see players being taken off the pitch if they were subjected to racist remarks.
"I think it's disgusting," one fan said before adding, "apart from expecting black players to stand up and complain, I want to see some white players standing up and complaining."
He added: "I'd be quite happy to see the manager simply taking players off the pitch."
Another fan said: "It's not fair for the club or the fans to suffer ... I do think they need to make examples of the ones they do catch doing it."
A third added: "I totally agree with Harry Kane who said he'd lead players off the pitch."
The "No Room for Racism" campaign is also designed to mark the contribution made by the previous "Kick It Out" campaign, which was formed 25 years ago.