Media reports have suggested there was a row between the coaching staff and players when they met up at the training ground the day after last Saturday's disappointing 2-0 defeat at Everton in the Premier League.
After the game Villas-Boas described it as Chelsea's worst performance of the season.
Asked whether he still had the support of his players, the manager told a news conference on Thursday: "They don't have to back my project, only the owner needs to back my project."
Villas-Boas, speaking ahead of Saturday's FA Cup Fifth Round match against second-tier Birmingham City at Stamford Bridge, denied there was a row during Sunday's get-together.
"There was a meeting of technical staff and players, nothing dramatic," he explained.
"Everybody understands we need more [than we are giving] and responsibility for this must be shared between the players and management. The right results haven't been happening for us for quite some time."
Chelsea won the FA Cup and Premier League double in 2010 under former coach Carlo Ancelotti but are now fifth in the top-flight having won only two of their last 10 league games.
They are on the same points as fourth-placed Arsenal but with an inferior number of goals scored, leaving the West London club outside the qualifying places for next season's Champions League.
NO PANIC
Villas-Boas, appointed in the close season to replace the sacked Ancelotti despite only having one term - albeit highly successful - as a coach at Porto, said he was unaware of any concerns from his players over team tactics.
"Not that I know of," he said. "There is no panic, one thing is very important and that is that things are very tight between fourth and seventh places.
"These positions will change on a weekly basis and I am not going to discuss the need to finish fourth every week. There is a minimum damage limitation - Champions League qualification - and that is what we have to do."
Abramovich spent several days at the training ground last week but has been absent in the lead-up to the Birmingham game.
Asked if his position was under more threat than it was a week ago, Villas-Boas replied: "I don't think so but it's a question you'll have to ask the owner."
The Portuguese also answered questions about the fact some of the Chelsea players are in regular contact with their former manager, Real Madrid's Jose Mourinho, via text messages.
Villas-Boas said he himself also exchanged texts with some players from his former clubs at Porto and Academica.
"This is normal and I don't have a problem with it," he added.
Villas-Boas said captain John Terry trained fully on Thursday despite his persistent knee problem but hinted he may hold the defender back for Tuesday's Champions League first knockout round first leg at Napoli.
Strikers Didier Drogba and Salomon Kalou, in the Ivory Coast team beaten by Zambia in Sunday's Africa Cup of Nations final, are also likely to be back in contention for the Napoli match.
Injury will keep defender Ashley Cole out against Birmingham but midfielder Ramires is ready to return after a spell on the sidelines.
