Zanetti faces six months out after snapping his Achilles tendon on the weekend.
Ranocchia said: "We're all so upset because it's a long and painful injury. I've been through one myself, so I know what it's like.
"We're also sorry because he's our captain, he has been ever since I was born, and he's an example to us all. But with the physical and mental strength he's got, I'm sure he'll be back soon."