The 54-year-old became the 16th permanent managerial appointment made at Vicarage Road since the Pozzo family took ownership of the club in 2012.
The ex-West Ham boss replaced Rob Edwards at Watford on Monday.
"Not just at Watford but in the world of football, you have to deserve time, you have to buy time," Bilic said.
"How you buy time is with good work and the results.
"Do you think they appoint the manager to sack them? No, they appoint the manager to have success.
"Even this situation, when everyone is talking about Watford sacking managers - I'm number 16 or 17 or whatever - I'm in a good position because they definitely don't want to sack me. They want me to do good."
Bilic, who guided West Brom to promotion to the Premier League in 2020 during his last stint working in England, said he is used to dealing with questions about the lack of job security in management.
"It's quite common unfortunately for us, for managers," he said.
"It's normal you know and Watford are not the only ones that have changed manager so far in England and not to mention Europe.
"The most important thing is they [owners and club bosses] have clear ambition and they give you - and I feel it so far in these very early days - they provide you with everything you need and all they can to be successful."
The former Croatia national team manger said he is "rested and recharged" after nine months out of the game, having left Chinese side Beijing Guoan in January.
He takes over a Hornets side that are 10th in the Championship after 10 games back in the second tier after a solitary term back in the Premier League.
"It feels great," Bilic said of taking the Watford job.
"I'm back in England, I'm back in a really good league an back at a top club with clear ambitions.
"This is one those opportunities that I was really looking for and also a club that I was interested in. I'm here and I'm very optimistic and positive."