Excrement was found on the floor of the Eagles' dressing room ahead of the second-leg clash between the fierce derby rivals last Monday.
In an email sent to season-ticket holders this evening, Brighton chief executive Paul Barber confirmed the club had formally apologised to Palace and vowed to tighten security at the ground.
However, Barber said he could not comment on the suspension of manager Gus Poyet, assistant Mauricio Taricco and first-team coach Charlie Oatway - for matters unrelated to the dressing-room incident - following the Seagulls' 2-0 defeat.
"It's clearly been a challenging week for our club," wrote Barber.
"Defeat at home to our biggest rivals in a play-off semi-final; the suspension from work and pending investigation of three members of our staff; and the revelation of an unsavoury incident that took place in our visitors' dressing room last Monday.
"These events have led to some unwelcome headlines that we all would have preferred not to have been reading during the last week. Understandably, many supporters have asked me, both in person and in writing, about recent events - and, in particular, how and why they have happened. At this point, I'm unable to give you answers to all the questions you may have.
"What I can say to you is that every football club faces a variety of challenges at different points in its history. We are no exception and I can assure you that we will address each of these challenges as you would expect and want us to, namely, professionally and with as much as dignity as possible.
"We apologised to Crystal Palace as soon as the vandalism in their dressing room was discovered, and again more formally a few days after the match. As a result of what happened, please rest assured we have reviewed our internal procedures to guard against this ever happening again.
"On other matters, you will appreciate that I'm unable to comment further at this time."