Brighton and Hove Albion head coach Graham Potter said it was "sad and unacceptable" after two visiting Wolves fans were arrested for homophobic abuse at the Amex Stadium last Sunday.
The arrests came on the same weekend Premier League clubs - including Albion - backed Stonewall's Rainbow Laces campaign.
"It's unacceptable," Potter said. "It's sad that we're even having the conversation. If we want to do anything and if we want to change anything, football should be football for everybody, regardless of their ethnicity, their religious position or their sexuality.
"But you can see in many instances that that's the world we're in at the moment and football has to do its best to try and lead the way."
Stonewall's initiative was held at the Amex last Sunday against Wolves. Rainbow laces were handed out to the crowd, players wore rainbow laces and armbands and a whole section of the stadium held up cards ahead of the match to provide a rainbow.
The charity was launched in support of gay, lesbian, bisexual and transgender people in sport.
On the same weekend Everton investigated reports of homophobic chanting towards Chelsea fans at Goodison Park.
Brighton face Crystal Palace at Selhurst Park in the Premier League on Monday.