A "minority" of fans in the home end closest to the visiting Seagulls supporters are alleged to have sung the offensive chants, prompting Foxes fans to take to social media after the match to voice their concerns.
A club spokesman told the Leicester Mercury: "We are committed to creating a passionate, inclusive, welcoming environment at King Power Stadium, in which everyone is free to enjoy the matchday experience.
"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."
Shinji Okazaki opened the scoring within the first two minutes against Brighton before Harry Maguire added a second in the 54th minute to give the Foxes their first win of the new Premier League season.