The match, on Jan. 8, comes a few weeks after there were chaotic scenes in the Premier League match between the sides at Brighton's Amex Stadium, where hundreds of Palace fans were denied entry to the stadium.
Six people were arrested and two stewards injured when fans without tickets stormed a turnstile at the Amex.
"We raised concerns about playing the league match between the two clubs at night, as there have been previous issues when we played evening games in the Championship, but felt we were presented with a no option scenario," a Palace statement said.
"Given the events that occurred, we assumed that this time what we considered to be good sense would prevail and the game would be scheduled as an early daytime kickoff."
Palace are also upset by a ticket allocation of 2,000 for their fans, saying they should be allocated more than double that total under normal FA Cup rules.
"We completely understand the security concerns around this match and the safety of all supporters must be paramount," Palace said.
"It's for that very reason that we felt the best and most obvious solution, as is the case with other big, highly-charged derby games, would have been a lunchtime kick-off, combined with a bigger ticket allocation to cater for the overwhelming demand from our fans, many of whom will again be left disappointed."
Despite being 46 miles apart matches between Brighton and Palace have taken on 'derby' status and emotions ran high during last month's 0-0 draw between the sides.
(Reporting by Martyn Herman; Editing by Toby Davis)
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