Mazzarri hails 'bionic champion' Zanetti
The 40-year-old captain and defender came on in the 82nd minute, six months after rupturing his Achilles tendon.
Mazzarri was full of praise for Zanetti and said several of his players could learn from the former Argentina international.
"Zanetti has something special and you can see why he's a world-class champion," Mazzarri told Sky Sport Italia.
"While the team was suffering, he came on for 10 minutes and gave everyone a sense of calm.
"To come back at his age after such a long lay-off and be immediately so confident, it's extraordinary. He's bionic."
Inter took a 30th-minute lead at the San Siro when Livorno goalkeeper Francesco Bardi failed to keep out a Jonathan cross from the right.
The hosts sealed the three points in the first minute of additional time as Mateo Kovacic's tricky run led to Yuto Nagatomo's goal.
Mazzarri said the visitors deserved credit for their performance and urged his team to improve on their efforts.
"To be honest, I had the utmost respect for Livorno and that has increased today. They are organised, strong, sharp and made us suffer tonight. They deserve praise," he said.
"With the way we were playing in Udine (in a 3-0 win over Udinese last time out), I expected something more vehement from my men tonight.
"We weren't sharp enough and were always second to the ball behind Livorno, while at times we made some defensive errors."