Two Foxes fans were arrested during their team's 2-0 home win over the Seagulls on Saturday.
Brighton Supporters Club's vice chair said such chanting was "disgusting" and the club should be fined and anyone responsible banned from the stadium.
The chairman of Foxes Pride said abuse was "offensive" and "unacceptable".
Brighton is a city well known for having a substantial lesbian, gay, bisexual and transgender (LGBT) community.
Liz Costa from Brighton & Hove Albion Supporters Club said about 50 Leicester fans took part in the "disgusting" chanting throughout most of the match at the King Power Stadium.
She said: "The club needs fining, this has nothing to do with football.
"[The chanting] lets the whole club down and damages their reputation. I feel I never want to visit [the stadium] again.
"Those responsible need to be identified and banned."
She added that Leicester's stewards were "very good" and reacted quickly.
Graeme Smith from Foxes Pride said: "There are some forums where people are saying you need to get over it, you need to get a life, it's only a bit of banter, but its not, it's offensive and it's unacceptable."
Leicester fan Chris Whiting, who is gay, said the "shocking" chanting by his fellow supporters made him feel unsafe.
Both the Football Association and the Premier League have been approached for comment.
Paul Mortimer from anti-discrimination group Kick It Out said: "It's about education more than anything, making people aware of the impact that this has on their own fans.
"Within football clubs there are LGBT communities and imagine what they will be feeling when a section of fans are saying this horrible language in their presence."
Leicester City said it was "disappointed" about what happened but satisfied stewards reacted "swiftly and appropriately" and those responsible were ejected and reported to police.
A 44-year-old man has been charged with indecent chanting under Section 3 of the Football Offences Act and is due to appear at Leicester Magistrates' Court on Thursday.
A second man aged 21 who was arrested on suspicion of making obscene gestures was given a caution.

Speaking during a parliamentary debate, Philip Hollobone said individual fireworks are extremely dangerous.
But business minister Jo Johnson dismissed a ban and insisted current laws work well.
The debate came after a petition to restrict the use of fireworks attracted more than 100,000 names.
The petition, which called for restrictions on when fireworks can be used, was started by Jill Cutsforth, from Beverley, East Yorkshire, and Julie Doorne, from Sleaford, Lincolnshire in a bid to reduce stress and fear in people and animals.
But, Mr Hollobone, MP for Kettering, called for the government to go further.
He said: "I think there's great merit in saying all fireworks displays need to be licensed with a licensed operator, and frankly, amateur family-organised fireworks displays in people's back gardens are basically rubbish."
Labour's Angela Smith, a member of the the Environment, Food and Rural Affairs Committee, also backed the petition, arguing that restricting the number of days the public and organised events can set off fireworks should be restricted.
She said: "Ideally, we would end the use of fireworks in back gardens. But I do understand the difficulty in delivering that as policy."
Instead, she called for tighter regulations to govern how people use fireworks.
Mr Johnson acknowledged the concerns raised but said restricting their use to traditional holidays would be ineffective.
"It is likely that those who already use fireworks in an anti-social or inconsiderate way would not be deterred by further regulation," he said.
He added: "Restrictions in use could lead to a drop in legitimate sales, leading to job losses not only in the firework industry but independent and associated businesses."
Bracknell MP Phillip Lee also warned the debate that restricting the number of days that displays are permitted could reduce the viability of well-performing fireworks businesses.
The government said following the debate it would continue to monitor the situation closely.
Supporters of both clubs have condemned homophobic abuse after anti-gay chanting was heard during Leicester's match against Brighton.
[NEXT_CONCEPT]
Amateur home firework displays should be banned, in favour of licensed organised displays, a Tory MP has suggested.