Club president Enrico Preziosi revealed he had decided to act following the loss and identified former Juventus coach Luigi Del Neri as De Canio's favoured replacement.
Genoa led Roma 2-0 after 15 minutes of yesterday's game only to lose 4-2, a result which leaves them ninth in the table and 13 points behind leaders Juventus.
Preziosi told the ANSA news agency: "At this time it was right to change, I immediately took Del Neri because I was afraid he was going to be somewhere else. Reinforcements arrive in January."
De Canio, formerly coach at Chievo, Roma and Juventus was hired in April to replace Alberto Malesani and helped Genoa avoid relegation but a poor start to this season has led to his departure.