Villas-Boas had to answer questions about his future last week after Spurs lost 6-0 at Manchester City.
A host of pundits, including Gary Neville, Alan Shearer and Jamie Carragher, all criticised Villas-Boas and his team in the wake of the thrashing.
Former Spurs chairman Lord Sugar also criticised Villas-Boas' tactics earlier this week, but Dembele is standing firmly behind his boss.
Asked if the recent criticism of Villas-Boas had been fair, the Tottenham midfielder said: "No, of course not. The manager is working hard to give everyone confidence.
"The Man City result was not only embarrassing for the manager, but for us as well. People were laughing at us after that performance."
And there appears to be no doubt that the Spurs squad are fully behind their manager.
"Of course (we are)," Dembele added.
Dembele is not alone in that respect, either. His midfield partner Sandro says Villas-Boas is a popular figure among the players.
"Everyone likes him," the Brazilian said.
"We have to play for him and I think everyone is doing that on the pitch.
"Criticism happens to any coach if you do not win games. He knows we are here and we showed him what are going to do.
"I play for him every game. And for the club."
The pressure eased on Villas-Boas slightly on Sunday after Tottenham put in a much-improved performance to claim a 2-2 draw against Manchester United on Sunday.
The team's passing was more slick, their tempo increased, and some of the players who previously had question marks over their heads turned in good displays.
Paulinho and Roberto Soldado put in good shifts while Kyle Walker found the target with a clever free-kick and Sandro scored a stunning 25-yard strike which started outside the right-hand post and drifted back into the top corner past a dumbstruck David De Gea.
Although Spurs still could do with a win to pull them closer to the top four, Sandro is relieved that the pain of the 6-0 hammering at the Etihad Stadium has faded somewhat.
"We played well, we played together," said the 24-year-old, who has looked good this term following his recovery from a serious knee injury.
"Last week was the worst week I have had in my career. I have to take this out of my mind.
"As a team we have to stay together in the bad moments and I think we are doing this. Everyone stayed together, talked and it was good."
Spurs know the next few weeks will be crucial to their chances of clinching the Champions League qualification spot that eluded them last season.
The Londoners have tricky fixtures against Liverpool, Southampton and Manchester United over the next month, but they will be big favourites to return to winning ways at Fulham on Wednesday.
The Cottagers, who sacked manager Martin Jol and replaced him with Rene Meulensteen on Sunday, have lost their last six games but Dembele, who spent two years at the west London club before moving to Spurs, expects a tough derby.
"It is never easy in the Premier League," the 26-year-old said.
"I like the club very much so I hope they do good. But on Wednesday, I want us to win of course."