The club confirmed a number of home fans were ejected from the stadium by stewards and Leicestershire police say they are reviewing evidence to see if others were involved.
According to eyewitnesses, the abuse began in the closing stages of the game the hosts won 2-0.
“In the last 20 or so minutes the chanting started towards the Brighton fans and then after that it got a bit more nasty with a few isolated shouts, which were a bit more malicious,” Leicester fan Chris Whiting told the BBC.
“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.”
A Brighton fan, who did not wish to be named, told the Leicester Mercury the abuse was “like something out of the 1970s”.
“We’ve encountered abuse over the years, but it’s all but gone from the game,” the away fan said.
“However, a group of around 20 to 30 Leicester City fans close to Brighton supporters suddenly started chanting vicious homophobic abuse and making homophobic gestures.
“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.”
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 matchday experience," a club spokesperson said.
"As part of our ongoing efforts to educate our staff, senior 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.
"While disappointed that such abuse took place during Saturday's match, we are satisfied that our stewards reacted swiftly and appropriately, which led to the responsible minority being ejected from the stadium and reported to the police."
Kick It Out's professional players engagement manager Paul Mortimer said education was needed to prevent supporters using homophobic language.
Mortimer told BBC Radio Leicester: "How much of a problem it is we'll see as the season goes on but it's definitely there and it's something that football as a whole has to work together to quell.
"People need to recognise the impact that it has on fans.
"It's about education more than anything - making people aware of the impact that this has on their own fans.
"I would bang the drum of education more than anything else, because 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.
"It's unacceptable and I'm sure if it carries on there will be sanctions."
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