Abramovich has fired every manager to have ended a campaign empty-handed since buying the club more than eight years ago.
But Villas-Boas insists the Blues' billionaire owner has assured him his job is safe, even if he does not deliver silverware come May.
Speculation has been rife that Villas-Boas will not last that long unless he arrests Chelsea's poor start to the season.
Having been dumped out of the Carling Cup by Liverpool two days ago - albeit with a youthful team - Chelsea could find themselves out of the Champions League on Tuesday if they do not win, or keep a clean sheet in their final Group E match against Valencia.
Failure to reach the last 16 would be unprecedented during the Abramovich era and compound a start to the Barclays Premier League that sees Chelsea 10 points behind leaders Manchester City and outside the top four.
They could lose even more ground if they do not win at Newcastle on Saturday or beat City at Stamford Bridge on Monday week.
That would leave them in the kind of position that has seen Abramovich pull the trigger in the past, but Villas-Boas is adamant he will not suffer the same fate.
And the 34-year-old declared he has been told his job is safe even if Chelsea go a second successive season without a trophy for the first time under Abramovich.
"I have that assurance," Villas-Boas said, despite admitting such a campaign would amount to "a failure".
He added: "Conversations have been ongoing with the board and they have been fully supportive."
Villas-Boas cited his three-year contract as proof his head was not on the block, and although compensation payments have never prevented Abramovich wielding the axe in the past, jettisoning a man he paid Porto more than £13million for during the summer would be hugely embarrassing for the Russian.
It would also defeat the purpose of Villas-Boas's appointment, which was to transform the way Chelsea play while continuing to win silverware.
"There are no schedules for achieving different kinds of things," said Villas-Boas, whose side have recorded two wins and five defeats in their last nine games.
"We are not avoiding our responsibilities towards this year, that is for sure. If we fail this year, like we failed last year, we were not up to our standards, so we need to see where we missed.
"And if we look back at our position that we finish in the league at the end of the season, we would look back at this period always as a period when we might just have lost track of our points."
Villas-Boas reiterated he would not change his attacking philosophy in pursuit of results and again insisted his players were fully behind his approach amid fresh reports of dissent.
He added: "They will never lose faith because the philosophy is not a cancer of this football club, the philosophy is not the reason why we are losing games, it's a misconception.
"Philosophy is playing good football for the fans, good football to try and win games. We have been trying to that."
Asked how he could be certain his players would not lose faith even if what he has repeatedly dubbed the "negative spiral" continued, Villas-Boas said: "Because they are with me. They are with me and believe in what we are doing."
The only man's faith that matters, of course, is that of Abramovich amid what is undoubtedly the biggest test of Villas-Boas's fledgling managerial career.
Villas-Boas said: "I don't care if it's my best time or worst time as a football coach, this is about the football club, not me."
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