The incident led stewards and Sussex Police to close the gates six minutes after kickoff as around 150 Palace fans, some with valid tickets, were denied entry and escorted back to the train station.
"The disorder was caused by a minority of individuals who attempted to gain entry to the stadium without tickets," Brighton chief executive Paul Barber said on the club's website (www.brightonandhovealbion.com).
"Thanks to the swift action of the club's stewarding team, supported by Sussex Police, we avoided further, major disorder - and while some genuine fans were left extremely disappointed and unable to get into the stadium, the correct decisions were made.
"I'd like to thank the majority of fans of both clubs for their good behaviour and patience in complying with the instructions of our stewards and police."
Brighton said several stewards suffered minor injuries and one from each club was hospitalised following the scuffle.
The club will share CCTV images of suspects with Sussex Police, the Metropolitan Police and Crystal Palace to help with identifying those responsible.
Palace issued an apology on Wednesday in which they condemned the incident and offered a refund for any supporters with legitimate tickets who were denied entry to the away end.
"This kind of antisocial and criminal behaviour is completely unacceptable and we condemn it in the strongest possible terms," Palace said on its website (www.cpfc.co.uk).
"There are very clear images of the incident and we will work with the police to identify the supporters involved, who will face stadium bans as well as potential criminal proceedings."
The draw dropped Brighton to 10th in the league as they prepare to host Liverpool on Saturday, while Palace stayed rooted to the bottom of the table.
(Reporting by Aditi Prakash in Bengaluru; Editing by Christian Radnedge)
