The veteran defender believes the San Siro club can play a big part in the Serie A title race and hopes to be back in action sooner rather than later
The 3-0 reverse at home to league leaders Roma was the Nerazzurri's first defeat of the Serie A season, but they remain in fourth place after the opening seven rounds of matches.
"I'm not surprised by Mazzarri's ability, I knew him as an opponent," Zanetti was quoted as saying by Tuttosport. "[Rafael] Benitez was with us for a short time, but you knew he was very good. Unfortunately we had a lot of injuries.
"The important thing is that we're in a new situation and hope to be protagonists [in the title race] - this is the first goal Inter have to think about.
"There are so many teams fighting for the title. Roma, for example, have great players. We will see what will happen in the end, the championship is very long."
Italian football has been embroiled in a debate over the recent stadium ban issued against AC Milan following discriminatory chants against the south of the country.
The Rossoneri were initially ordered to play Udinese behind closed doors at San Siro on October 19 after fans were found to be demonstrating "territorial discrimination" though the sanction has since been suspended as prosecutors await further evidence following the club's appeal.
Zanetti believes there must be clearer guidelines on what is deemed a punishable offence when it comes to supporter chanting.
"There must be clear rules. I think this is the only way football can move forward," said the 40-year-old.
Finally, the Argentine hinted he could soon return to action after a lengthy spell on the sidelines with an Achilles injury.
"I'm better, I think I'm in the last phase of my injury. I hope to return soon and make myself available."