Despite beating Sampdoria 1-0 at San Siro on Thursday, the Nerazzuri were ousted from the competition after they lost the first-leg 3-0 in Genoa.
"It is true that tonight I was very angry," Cambiasso told Inter TV.
"If an opponent who is playing away from home urges the fans on as much as Cassano did tonight, then that is very irritating.
"Once or twice, here and there, is understandable, but to do so in every game, it seems like he is making a mockery of it.
The Argentine, who was disappointed at the Cup exit, confirmed that the first-leg loss made it a mountain for Inter to climb in the second.
"The defeat was due to the poor performance in the first leg at Marassi," the former Real Madrid added.
"We couldn't score in the first leg because we didn't take our chances and the same thing happened again."
Inter now only have the Serie A title to win, after they previously crashed out of the UEFA Champions League.