"I don't feel under pressure because I speak with the owner every day," Mazzarri told British media. "We know what our objective is and we're not only looking at the next five or six matches, we are looking at the next three years.
"When you look at all the injuries we have, it is difficult to get results in the Premier League. Now we have to take this occasion to look and work for the future."
Mazzarri is the eighth manager to work at Vicarage Road under the club's Italian owner Gino Pozzo, whose family took over in 2012.
Watford, placed 14th in the league after 20 games, have had five managers in the past three years.
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"The important thing is to keep fighting for the next games," Mazzarri added.
"I liked the way our fans behaved because they understood the moment we're in and they supported us until the end and this is very important for us."
Watford host second tier side Burton Albion in the third round of the FA Cup on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
