The London outfit surprised many by comfortably securing Premier League survival under the stewardship of Tony Pulis, who took over in November following Ian Holloway's departure.
Palace are now preparing for a second season in the top flight and announced their retained list on Wednesday.
A total of 12 players have been released by the Selhurst Park club, with defenders Gabbidon, Moxey and Parr all departing.
Striker Aaron Wilbraham has also left Palace after a two-year spell.
However, Palace are keen to retain the nucleus of the side that kept them in the division, and are in negotiations with the out-of-contract trio of Julian Speroni, Marouane Chamakh and Kagisho Dikgacoi.
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