The Premier League side's new manager also revealed at his unveiling that the club plans to sign "two or three" more players.
Mazzarri, 54, was in May appointed as the successor to Quique Sanchez Flores, who was sacked despite a promising first season in the Premier League.
He was known in Italy for his willingness to smoke when sat in the stands, but dismissed reports he did so in the dressing room at half-time of their pre-season fixture with QPR.
The Italian explained, however, that for all of his enjoyment of smoking, it is a habit he would not let his players indulge in.
"I wouldn't allow any player, not even my son, to smoke," said Mazzarri, whose predecessor Sanchez Flores was popular among Watford's players.
"Because of the job I do, sometimes in life there are moments where small things make you feel better
One of them, for me, is smoking
I'm the first to admit it's not good.
"I consider myself the boss of the group
For me, it is very important
There have to be some rules, there has to be mutual respect in a group.
"Victory comes from these principles: respect of the rules
I'm like the father of the family
It's almost like a father-son relationship."
Mazzarri's first competitive fixture in charge of Watford comes at Southampton on Saturday
He revealed he had been present at their FA Cup semi-final defeat against Crystal Palace last season, when speculation began to build regarding Sanchez Flores' likely departure.
According to Mazzarri, Watford's owners the Pozzo family had in the past expressed an interest in recruiting him
He also insisted that they are willing to trust his judgement.
"There is the possibility to go ahead for an extra two or three players, they said it's no problem if we need them and I think we do," said the former Napoli and Inter Milan manager, who spoke via a translator.
"I prefer not to go too much into detail but it will probably be one defender, one midfielder and one forward, although it could be two in one position.
"I've known the Pozzos for some time
There has always been a mutual good relationship.
"There have been times in the past when (Gino Pozzo) wanted to work with me but for some reason it didn't happen."
Source : PA
Source: PA