Both players will miss the remainder of the campaign, meaning Roma could struggle for a Champions League place
Sports judge Gianpaolo Tosel inflicted the punishment on both players after the Lega Calcio's disciplinary panel gathered on Tuesday afternoon to deliver their verdict.
Barring a subsequent appeal from Roma, both players will not be able to play against AC Milan, Catania and Sampdoria.
The statement from the Lega said the decision was taken against De Rossi for "having elbowed an opponent three minutes into the second half at the San Nicola."
Perrotta was sent off "for punching an opponent towards the end of the game."
Roma welcome Milan on Saturday night at the Olimpico. Vincenzo Montella's men are a point behind Lazio who are fourth.