The Hornets have won just one their last seven matches and slipped to 13th in the table on New Year's Day after a 4-1 home defeat to Tottenham.
Watford sit eight points clear of the relegation zone and some of the club's fans greeted their latest loss with boos, having grown frustrated with recent performances.
Mazzarri's cause has not been helped by a number of injuries to key players, not least Camilo Zuniga, who felt pain in his ankle during the warm-up against Tottenham and had to be replaced at the last minute by Odion Ighalo.
Despite their recent issues, Mazzarri remains steadfast in his belief he is the right man for the job and is not concerned by the increasing threat of relegation.
"From the first day I arrived I spoke with the club and the president," Mazzarri said.
"When we have spoken about the first objective, which has always been the same, it was to avoid relegation. In this moment if we look at the table we are doing even better than the starting objective.
"We could have been where Crystal Palace are or other teams are but we aren't. This has always been the first objective and we're doing okay."
Watford were ninth with 29 points at this stage last season under Quique Sanchez Flores, who was sacked by the club's owners in the summer.
Mazzarri's team are four places worse off with seven points fewer but the Italian insists comparisons with his predecessor are unfair.
"What happened last year, I'm really not interested," Mazzarri said.
"Last year I know in the first half Watford did very good and then in the second they started to lose some points. If we look at this year we're still on line with our objective which is to stay in the Premier League.
"Then if we really want to compare the Premier League this year to last it's much better than it was last season."
Watford last week