The Bianconeri ran out 2-1 winners at San Siro, but some gloss was taken off the victory when Giovinco was caught by a bad tackle from Esteban Cambiasso deep into stoppage time, an incident that earned the Argentine a straight red card.
The 26-year-old Giovinco limped off the field after the game and confirmed to Tuttosport that he is a doubt for the Champions League quarterfinal first leg in Germany.
"My ankle hurts and we are a little worried," Giovinco said.
The Derby d'Italia defeat leaves Inter in seventh in Serie A, and the frustration in Cambiasso's lunge was evident, though the Nerazzurri midfielder was quick to repent.
"Yes, I apologized to him [Giovinco] and I think that is the most important thing," the 32-year-old Cambiasso said. "I am sure that Sebastian understood. Anyone who has played football knows that if you wanted to hurt someone, you wouldn't go in as low as that. I arrived a split-second late."
Inter manager Andrea Stramaccioni was also quick to leap to his player's defense, suggesting that his character was not in any way malicious.
"I have already told everyone that Esteban is a good man and a true professional," Stramaccioni said. "No one needs to lecture him about this."