Brighton & Hove Albion chief executive and deputy chairman Paul Barber called for the crackdown after three people were arrested following the club's 1-1 draw against Chelsea.
Sussex Police confirmed that two fans -- one home and one away -- were arrested for homophobic abuse and one home fan was arrested for racist abuse.
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'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 told the Brighton website on Thursday.
'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.'
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Barber also urged fans to immediately report discriminatory behavior they experience at the club's stadium.
In a statement to CNN, Chelsea said that the club 'welcomes and commends the swift and firm action taken by Brighton,' adding that 'we join them in condemning the disgusting behavior of a small number of supporters at yesterday's match.'
It continued: 'Chelsea FC also operates a zero tolerance policy towards racism, homophobia and any other form of discriminatory behavior, and will always take the strongest possible action against season ticket holders or members who take part in such despicable behavior.'
Rainbow Laces campaign
The arrests made on Wednesday were the latest in a series of incidents of abuse that have blemished the Premier League.
It's the second time in as many months that Brighton has thrown out fans for homophobic abuse after two visiting Wolves fans were ejected in December.
That same weekend, Everton also launched an investigation after claims of homophobic chanting in the club's victory against Chelsea.
In December, the Premier League worked with anti-discrimination organization Stonewall to promote its Rainbow Laces campaign and show support for LGBT people in football and beyond.
The rainbow symbol -- synonymous with the LGBT movement -- was displayed on LED boards, captains' armbands, corner flags and even the laces of footballers over the course of two match weeks.
'It's really important that Brighton & Hove Albion stepped up and took action to show that hateful slurs are unacceptable and the club is committed to creating an inclusive environment,' Robbie de Santos, director of sport at Stonewall, told CNN in a statement.
'The more players, fans, clubs and organizations that stand up for equality in sport, the sooner we kick discrimination out and make sport everyone's game.'
The Premier League did not immediately respond to CNN's request for comment.
READ: Paul Pogba to have operation following ankle injury '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.' The arrests made on Wednesday were the latest in a series of incidents of abuse that have blemished the Premier League. READ: Paul Pogba to have operation following ankle injury '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.' READ: Paul Pogba to have operation following ankle injury READ: Paul Pogba to have operation following ankle injury Sussex Police confirmed that two fans -- one home and one away -- were arrested for homophobic abuse and one home fan was arrested for racist abuse. 'It's really important that Brighton & Hove Albion stepped up and took action to show that hateful slurs are unacceptable and the club is committed to creating an inclusive environment,' Robbie de Santos, director of sport at Stonewall, told CNN in a statement. '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 told the Brighton website on Thursday. Rainbow Laces campaign In December, the Premier League worked with anti-discrimination organization Stonewall to promote its Rainbow Laces campaign and show support for LGBT people in football and beyond. 'It's really important that Brighton & Hove Albion stepped up and took action to show that hateful slurs are unacceptable and the club is committed to creating an inclusive environment,' Robbie de Santos, director of sport at Stonewall, told CNN in a statement.
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