The Argentine full-back is expected to be sidelined for up to eight months, with many suggesting that the 39-year-old's career is over.
"I believe everyone is entitled to their own opinion," he told Inter Channel. "I'll say it again - my aim is to recover, undergo physio with the medical staff, which is the one of the best around. Then, when I feel better, I'll try to return to action. I think that after a career like mine, I'd like to at least play once more in front of my fans. And I hope it's more than one.
"I knew immediately that it was serious and it was maybe my Achilles. But it's happened, it was an unlucky day. As I've said, it comes with the job and it's come at this stage of my career, when I'm nearly 40.
"Thankfully I've not had many serious injuries over the course of my career, this is perhaps the first. I'll take my time, try to recover and, above all, to return 100% fit."
Zanetti picked up the injury in the first half of Inter's 1-0 away defeat to Palermo in Serie A on Sunday.