The club has earned only one win from its last five matches and slipped to 10th in Serie A after Sunday's loss.
Mangia was promoted from coach of the youth team in the preseason as a replacement for Stefano Pioli. But after signing a two-year contract extension with the club last month, the 37-year-old Mangia is out.
Sunday's defeat was the club's seventh in 15 league games this campaign, while Palermo has also been eliminated from the Coppa Italia by Siena on penalty kicks.
There has been no announcement from the club about who will take charge for Wednesday's match at Novara.