An early red card saw Bologna go down to 10 men, and Frosinone took full advantage to earn their second win of the season.
Relegation-threatened Bologna have fired Filippo Inzaghi and hired Sinisa Mihajlovic as its new coach.
Bologna made the announcement on Monday, a day after losing at home to Frosinone 4-0.
Inzaghi, the former striker for Juventus and AC Milan, was hired in June, while Mihajlovic's most recent job was with Sporting Lisbon, where he was fired nine days after being hired in June without coaching a single match.
Mihajlovic, whose contract lasts through the end of the season with an option for next season, previously coached Bologna in 2008-09 for his managerial debut in Serie A.
Mihajlovic has also coached Catania, Fiorentina, Serbia, Sampdoria, Milan and Torino. Bologna are in 18th place, three points from safety.
Source: espn.co.uk