The hosts won the game 2-0, but witnesses claimed that the abuse started in the latter stages of the Premier League clash.
Leicester said they were "disappointed" at the actions of the "responsible minority" but were confident their staff reacted "swiftly and appropriately".
A club spokesman said: 'We are committed to creating a passionate, inclusive, welcoming environment at King Power Stadium'.
"Naively I thought the days of homophobic abuse at Brighton fans was long gone, at least at our football club, it certainly hadn't happened for a good few years".
LEICESTER City have condemned the homophobic chanting that took place against Brighton.
"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".
Davis says Brexit trade agreement would progress border issue
It separately raised the idea of a "temporary customs union" with the EU after leaving the bloc. In effect, what they seem to be saying is that they want a customs union tailor-made for them.
Leicester also admitted a number of home supporters had been ejected from the game by stewards, who they said had undertaken "specialist training" this summer to identify such abuse.
Kick It Out's professional players engagement manager Paul Mortimer said education was needed to prevent supporters using homophobic language.
"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".
Graham 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".
"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 disgusting language in their presence".
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