Luton Town have threatened to ban any fans found to have taken part in tragedy chanting during Sunday's 1-1 draw with Liverpool.
The Hatters have launched an internal investigation after chants which indirectly referenced the Hillsborough disaster were heard during the match.
Luton "wholeheartedly" apologised to anyone offended by the chants, adding they are "extremely disappointed".
The FA is "seeking observations" from Luton and "further detail" from police.
The Premier League said it is "appalled" by the chanting heard at the match and "strongly condemns all forms of football tragedy abuse".
Luton said in a statement: "The club condemns any kind of chanting that knowingly seeks to divide, and our safety and security team launched an internal investigation at the earliest opportunity.
"What has quickly become evident is that a number of people may have taken part without knowledge that the words used were in relation to the Hillsborough and Heysel tragedies, and we see the route to persuading supporters not to repeat these chants in future is through communication and education.
"On this basis we are reviewing CCTV and media footage from the match, and will speak to witnesses to identify individuals who may have taken part. Any perpetrators could face stadium bans and potential criminal prosecutions."
It added: "On behalf of all at Luton Town, we would like to wholeheartedly apologise to anyone offended by the chants heard during yesterday's match, and will continue to work with supporter groups to educate fans on chants that are classed as tragedy abuse by football authorities, the police and CPS."
The Premier League also said it would be launching "education resources" to help tackle the issue.
Its statement added: "Football tragedy abuse causes significant distress to the victims' families and other football supporters. As part of the package of measures announced at the start of the season, the Premier League will launch education resources to help children understand the hurt and impact of negative behaviour such as tragedy-related abuse.
"From Monday, 13 November, this in-classroom lesson will be made available to more than 18,000 primary schools and 60,000 teachers in England and Wales as part of the Premier League Primary Stars programme."
BBC Sport understands Liverpool wrote to Luton prior to the Kenilworth Road club's statement to ask about the protocols the Hatters had in place to deal with tragedy chanting and what actions they would take.
The Reds also offered to work with them on education - as they are believed to have done with Leeds United, Manchester City and Manchester United - before the reverse fixture in February.
The Premier League condemned the chanting, adding in a statement: "We continue to treat this as an unacceptable issue and are committed to addressing it as a priority. Those found guilty of tragedy-related abuse face an automatic club ban and will be referred to the police."
Earlier on Monday, the FA said it is also seeking "further detail from the police", while BBC Sport understands Bedfordshire Police are talking to the club.
Meanwhile, Liverpool boss Jurgen Klopp said anyone involved in tragedy chanting "should be ashamed of themselves".
Ex-Reds defender Jamie Carragher was commentating on the game for Sky Sports and referenced the chanting during play, saying: "At the start of the season I was involved in something with supporters coming together about tragedy chanting.
"I've just heard that a couple of times in this game. As supporters, you've got to have rivalry, there is no doubt. But we're better than that.
"It's happened two or three times in the game. All clubs have been guilty of that over the years at different times. But the world we live in right now, I think we're better than that."
Klopp, who said he did not hear the chants himself, commented: "Shame on everyone who said it."
Klopp has previously spoken out against tragedy chanting between rival supporters, and in July the Premier League and English Football League issued a new charter outlining rules for dealing with the problem.
The introduction of the charter followed the arrest of a Manchester United supporter at last season's FA Cup final for wearing a shirt which mocked the victims of Hillsborough.
The Football Supporters' Association (FSA) said the chants heard during the second half of the Premier League draw at Kenilworth Road are "totally unacceptable".
"Tragedy chanting reared its head again yesterday," the FSA said on Monday. "Just because something horrible was chanted in the past, it doesn't give anyone a free pass to sing something horrible years later. Let's all draw a line in the sand."
The Premier League meeting was the first between the two sides since an FA Cup replay at Anfield in January 2008.