The midfielder's contract expired at the end of June, and he was keen to extend his one-year stay at Selhurst Park after helping Palace secure promotion to the Premier League last season.
But following talks with Holloway, the 27-year-old Brazilian was not offered a new deal and has now become a free agent.
"I sat down with the manager and told him what I wanted in terms of football. He said he didn't see me in his plans due to playing style conflict," Moritz wrote on his Twitter account.
"I appreciate his honesty and we decided to move on. At the age of 27, I'll need more game time.
"I wish everyone at the club success, I will miss the staff, fans and my heroic team-mates."
A statement on the Palace website read: "Moritz signed a one-year deal at Selhurst Park, which expired at the start of July - and the club have decided not to offer an extended deal to the player.
"Moritz made a total of 32 appearances for Palace last season, including coming on as a substitute against Watford in the Championship Play-Off Final at Wembley. He found the net on five occasions.
"Crystal Palace Football Club would like to place on record its sincere thanks to Andre for his service and commitment during the 2012/13 season. We wish him all the best for the future."