Three fans were arrested for racist and anti-gay abuse during Brighton's 1-1 draw against Chelsea at the Amex Stadium on New Year's Day.
A statement published on Brighton's website said that two home supporters were ejected, "one for racist abuse of Chelsea players and one for homophobic abuse aimed at Chelsea supporters."
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It added that "one visiting supporter was also ejected by club stewards for homophobic abuse aimed at home supporters. All three were arrested by Sussex Police outside the stadium and now face prosecution."
Brighton chief executive Paul Barber has suggested he would like to harsher punishments than a life ban in order to prevent similar issues from reoccurring in the future.
"Yet again our safety and stewarding team, along with Sussex Police, have had to deal with three separate and unwanted instances of disgusting racist and homophobic abuse," Barber said.
"If the prospect of a life ban from watching their clubs play football isn't a strong enough deterrent, we have to ask the question as to whether the courts should be given the power to hand out more severe punishments? Football can only do so much, and we are sick and tired of the game's reputation being tarnished by these people.
"I find it impossible to comprehend how and why some individuals think it's acceptable to behave in this way, and yet again I will make it very clear that neither Brighton & Hove Albion nor the wider football community, will tolerate racism, homophobia, or any other form of discrimination at any time.
"We would urge any fans confronted with similar discriminatory behaviour at our stadium to report it immediately, either directly to a steward or via our anonymous hotline, and we will continue to take the strongest possible action against such bigoted individuals. These people are not welcome at the Amex or at any football matches."
Meanwhile, Chelsea midfielder Christian Pulisic has said he needs to be more clinical following the 1-1 draw at Brighton, which damaged their battle for a top-four finish.
Asked what needed improving after the clash with Brighton, he told reporters: "It is doing a bit more to keep going, attack and create chances and just have that killer instinct. We are missing that a little bit.
"I can do better as well. Just being more clinical in the final third, finding the right pass or shot and scoring the goals. After we scored the first goal it was just about continuing and just not stopping there, making it two or three and putting the game to bed.
"That was it, we said at half-time that we had the chance to kill the game and we just weren't able to. We couldn't get the goal and in the end they found an unbelievable goal. It was not just us that were tired, it was the same for them. It's just about being clinical, experienced and knowing how to manage a game."