The 34-year-old Portuguese, who has overseen the club's worst start to a season since Russian Roman Abramovich took control in 2003, declined to comment on reports linking former boss Guus Hiddink with a return.
Instead, he made clear he believed he retained the backing of the owner and the players after "many meetings" this week. He said he felt sure that Chelsea could recover their winning form, adding: "Every game gives you an opportunity to get back on track and that's exactly our focus."
Chelsea have lost four of their last seven games, sliding to fourth in the Premier League, 12 points adrift of leaders Manchester City, and to the brink of possible elimination from the Champions League.
If they fail to win, or draw 0-0, when they meet Valencia in their final group game on December 6, Chelsea will not reach the knockout stages for the first time under Abramovich.
"It's life and death," he said. "We expect Leverkusen to do their job against Genk and qualify first. Then it's either Chelsea or Valencia in the last 16."
When it was suggested that he needed help, Villas-Boas said: "I don't agree... I don't solve problems on my own. I solve problems with my group of people and my group of players. Now, I just have to hold on to my self-belief and the belief of my players."
Hiddink, who enjoyed four successful months in charge at Chelsea in 2009 when they won the FA Cup, became a free agent after he failed to guide Turkey to qualification for the Euro 2012 finals.
Villas-Boas, the seventh Chelsea manager in eight years of Abramovich's reign, also hit back at critical comments made by former Chelsea midfielder Michael Ballack who helped Bayer Leverkusen to beat them 2-1 in the Champions League on Wednesday.
German Ballack said Chelsea lacked confidence and no longer had the formidable mental strength that had characterised their performances in past years.
"Michael has always been very self-opinionated," said Villas-Boas. "I disagree with him. He doesn't live in this dressing room. He used to live here before and he didn't solve all the problems before."
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