The Serbian defender joined the Nerazzurri on a free transfer this summer following the expiration of his contract at Manchester United.
Vidic impressed for his new club in Saturday's International Champions Cup penalty shootout success over Real Madrid and admitted afterwards that he is settling in quickly at Inter thanks to Mazzarri.
"I'm enjoying myself and I'm getting used to the style of play," the 32-year-old centre-half told reporters.
"[Mazzarri] is a coach who explains very clearly what he wants so it's easier to do what he asks of you."
Inter fell behind to Gareth Bale's long-range strike 10 minutes into Saturday's friendly in California but Mauro Icardi levelled from the spot and then slotted home the decisive spot-kick in the shootout.
It may only have been a pre-season match but Vidic took enormous satisfaction out of helping the Nerazzurri record a win over the European champions.
"It's always a beautiful game against Madrid, even if it's a friendly," the former United captain enthused. "It's even better to win a game like this."