The Italian club slumped to a disappointing ninth-placed finish in Serie A last season, a performance that cost Andrea Stramaccioni his job and led to Mazzarri's appointment.
The former Napoli coach has overseen a strong start to the new campaign, with his side having taken 10 points from their opening four games to claim third place in the Italian top flight.
And Mazzarri has expressed delight with his charges' start to life under his guidance.
"What matters most to us is how we play, how much improvement we make, how many mistakes we make," he said.
"What matters, besides the result, is that we go into games with the right approach and we're doing that very well.
"Of course we have ambitions, you always do, because you can always keep improving - that's precisely what we're looking to do.
"There are lots of players showing improvement in this team and they have the potential to achieve great things.
"The main thing is we try to stay fit and keep helping each other. I've got lots of options in this squad."
