After Italy's World Cup qualifying failure this week, Altobelli wants to see FIGC president Gabriele Gravina, team manager Gigi Buffon and coach Rino Gattuso all leave.
He told Tuttosport: "Simple, we didn't understand anything, the two previous eliminations didn't help to learn any lesson.
"That's why I say Tuesday's is the most serious elimination of all."
Asked about Gravina, Buffon and Gattuso, the former Inter Milan striker also declared: "Well, they are the ones who planned this technical project and usually when there are such big failures you take responsibility.
"Gravina chose Buffon, Buffon chose Gattuso."
On replacing Gravina, Altobelli nominated Inter president Beppe Marotta.
He said: "I would look good on Giuseppe Marotta as federal president. I'm not saying this because he's from Inter, the team where I played for so many years and have in my heart.
"I would have said it even if he was still at Juventus. He knows football like few others, he knows what he has to do."