Goals from Rodrigo Palacio, Andrea Ranocchia and Ricardo Alvarez secured three points for Inter, with Zanetti named in the squad for the first time since suffering an Achilles tendon injury in April.
While the Argentine was not called upon, Mazzarri does not feel it will be too long before the 40-year-old is back in action.
"I was uncertain whether to let Zanetti enter the pitch or not because his conditions seem to be very good," he said.
"During the training matches I've asked the other team-mates not to put him (under) too many pressures because he has just got back, but he seems so comfortable with the ball that he could have given his support ... if I had lined him up.
"Of course we have to be careful because he needs time. I can't tell precisely, but I believe that he may be available soon."
The victory over Udinese leaves Inter fourth in Serie A, nine points off leaders Roma.
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
Alexander Isak puts uncertainty over his Newcastle United future to bed amid fresh PSG and Arsenal links
