The Blues are fifth in the Barclays Premier League and look to be heading out of the Champions League following their 3-1 defeat to Napoli on Tuesday.
The 34-year-old's future has been the source of speculation over the last few weeks and reports have claimed there are rifts within the Stamford Bridge dressing room. But when asked whether he still has the backing of Abramovich, Villas-Boas told a press conference: "Yes. Of course."
Villas-Boas controversially left out Frank Lampard, Michael Essien and Ashley Cole for the first leg of the last-16 tie in Italy, which Chelsea led before a defensive horror show saw them concede three goals.
The Portuguese stood by his team selection, although he did admit that he had to explain why he chose the starting XI he did to the club's hierarchy.
He said: "No, I do not have any regrets about team selection... It was completely right. I have spoken to the persons near to him (Abramovich). He is disappointed and asking questions about how we set up the team, which were duly explained."
Former Liverpool boss Rafael Benitez, who has been out of a job since December 2010, has been linked with taking over from Villas-Boas, but the Spaniard's agent denied any approach had been made.
Manuel Garcia Quilon told Press Association Sport: "There is nothing official. It's only media speculation and we have not been approached by Chelsea. We would only evaluate that possibility once there is an offer."
Villas-Boas also denied reports that Cole had questioned his tactics against Napoli and insists he is not feeling the strain despite the club's failings on the pitch.
"It doesn't affect me at all," Villas-Boas said. "Last year I was linked with lots of different clubs whenever results didn't go [right for them], it is the same with this club."
Source: PA
Source: PA