Villas-Boas, who took over from Carlo Ancelotti in the summer, was forced to deny reports last week that some members of the Chelsea squad had become unhappy with his tactics. Recent defeats to QPR, Liverpool, Arsenal and Bayer Leverkusen had left the 34-year-old Blues boss under pressure, but he responded with a comfortable 3-0 win over Wolves at Stamford Bridge on the weekend.
Mata was the architect of the midlanders' downfall, setting up John Terry and Daniel Sturridge for the first two goals before adding his own on the stroke of half-time to seal the win. The Spain international was happy see his team return to winning ways after a difficult run, and rubbished talk of a rift between Villas-Boas and the team.
"It's never easy to have such negative results, but we all have a lot of faith in ourselves as a team. We have a lot of faith in our coach and in the quality of the squad," Mata said.
"We had a team meeting last week simply to reiterate that we are all together and that we are heading in the same direction and we showed that against Wolves.
"The group has always been very united, and we have always been sure that the secret in enjoying more success as we go forward, in getting out of this moment, has been to stay strong and stay together."
The Portuguese tactician was a surprise choice to replace the experienced Ancelotti given that this is only his second full season in management, but Mata claims the Villas-Boas' age will help the team's success, rather than hinder it.
"He is very warm with us, very close to us. He is roughly the same age as most of the squad, and that is a really good thing," Mata added. "He won a lot with Porto and that is what matters. He won every tournament he could win and having that experience at his age shows how good he is."
Fernando Torres was left on the bench for Saturday's win, with Villas-Boas preferring to use Didier Drogba as the head of a three-pronged attack with Sturridge and Mata. Torres, a British record £50 million purchase, has not scored a Premier League goal for two months, but Mata has backed his Spain team-mate to add more goals to his tally when called upon.
"He is very strong mentally," Mata said of Torres. "He is ready for the moment when the manager calls him and counts on him and I am sure he will score a lot of goals for us this season."