According to eyewitnesses, the abuse began in the closing stages of the game the hosts won 2-0.
"It made me very shaken, I felt a bit unsafe and very unwelcome in a place I've been going to since I was eight years old".
Openly-gay Leicester fan Chris Whiting, a season-ticket holder for 15 years, said: "I always thought if we ever experienced anything like that at Leicester, I'd be okay and I'd let it roll off my back".
A Brighton fan, who did not wish to be named, told the Leicester Mercury that the level of vicious homophobic abuse was a like a throwback to what football was like in England in the 1970s.
Leicester said they were "disappointed" at the actions of the "responsible minority" but were confident their staff reacted "swiftly and appropriately".
"We are committed to creating a passionate, inclusive, welcoming environment at King Power Stadium, in which everyone is free to enjoy the match-day experience", a Leicester spokesman said in a statement on Monday.
Leicester have confirmed stewards were forced to eject a number of supporters from the King Power Stadium for discriminatory chanting during the 2-0 win over Brighton on Saturday.
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"It was like something out of the 1970s, and this sort of bigoted, small minded behaviour needs to be stopped and those involved ejected from the ground".
King Power Stadium stewards undertook specialist training during the summer in effectively identifying offensive behaviour, including contributions from Leicester's LGBT Centre on recognising homophobic abuse.
He 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".
Kick It Out's professional players engagement manager Paul Mortimer said education was needed to prevent supporters using homophobic language.
"I think the club dealt with it really well and I'm glad they did because it shouldn't be allowed to go on".
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.
"It's unacceptable and I'm sure if it carries on there will be sanctions".