The two teams, who contest the M23 derby, met on November 28 at the Amex Stadium and on-duty officers wrongly reported that knives and knuckledusters were found inside the stadium.
A statement by the police force read: "The reference to weapons being found discarded at the stadium following the Brighton vs. Crystal Palace match on November 28 was based on information logged by our officers on the night and done so in good faith.
"Subsequently, it has been established that no such items were physically recovered at the stadium or in the city. We accept that this information was incorrect and the tweet published earlier today by one of our officers was wrong. Sussex Police apologises to both clubs and their supporters."
The game, which finished 0-0, was marred by crowd trouble before and during the match, with police saying that a small group of away fans forced entry into the stadium via the South Stand.