The tactician replaced Andrea Stramaccioni in the summer after the latter could only lead the Beneamata to a ninth-placed finish in Serie A.
Under Mazzarri, the Nerazzurri won their first two League games before drawing 1-1 with Juventus at San Siro on Saturday.
“I like Mazzarri, he knows what he wants and he's got personality,” the Argentine told Rai Due. “That's what you need at a big club.
“Inter-Juve was a good game between two strong teams,” he added. “There wasn't much between them.
“We played very well against an established side.”
Zanetti took no part in the game as he is still on the comeback trail after rupturing his Achilles tendon in April.
“I'm better now,” the 40-year-old explained. “I've started running again – I missed that! I'm still training on my own, but I'll have a test on Tuesday and if everything's ok I'll start upping the workload.
“I need to build up the calf muscle a bit. I'm not too far off returning – hopefully it will be around mid-November.”
Zanetti was Massimo Moratti’s first signing for the club back in 1995, the President who is in talks with Indonesian businessman Erick Thohir about selling the outfit.
“The Nerazzurri family will keep going,” Zanetti added. “Yet I can't imagine Inter without Moratti.
“It's true that there are negotiations under way and the President is deciding what's best for the Nerazzurri family, but knowing his feelings...
“In any case we'll see what happens when the negotiations are over. But, as I said, I can't see Inter without the Morattis.”
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