Some supporters jeered the Blues from the field at half-time of Saturday's 2-1 victory over West Brom, following a dismal opening 45 minutes in Villas-Boas' first home game in charge.
While the new Chelsea boss could understand fan frustration following a rare trophyless campaign last season, he urged them to show more patience for the remaining 18 league matches at Stamford Bridge.
"To go past a season in the Premier League, where you have to win it back, you need the full support of everybody," Villas-Boas said.
"Everybody must get involved.
"You must feel the presence of the public in a supporting way."
He added: "This team wants to be champions again. The public wants to be champions and demands it.
"We are listening to their demands and we want to perform but we need their full support all the time."
Villas-Boas felt the "anxiety" of supporters - sparked by Shane Long's fourth-minute opener - translated to his players, who failed to perform until a half-time pep talk.
The Portuguese insisted he had not felt the heat himself, despite staring his first league defeat for 16 months in the face at half-time.
Villas-Boas' Porto won the Portuguese title without losing a game last season and also claimed the Europa League but the 33-year-old revealed there were plenty of scares along the way.
"I think I suffered a couple," he said.
"It just happens. It's a game."
Villas-Boas also dismissed suggestions Fernando Torres was more anxious than most on Saturday, despite the ?50million man being substituted after once again failing to find the net.
He added: "I think it was a good contribution from everybody, to be fair.
"How many games have different behaviours from players from one half to another?"
Villas-Boas played down his own tactical changes, which involved throwing on matchwinner Florent Malouda before half-time and switching from a 4-3-3 to 4-4-2 formation, with Didier Drogba partnering Nicolas Anelka, who had earlier equalised.
"It's not a question of braveness, it's a question that maybe we wanted to surprise the opponent in some way," said Villas-Boas, whose side looked in need of the type of spark the likes of transfer targets Luka Modric and Juan Mata - the latter reportedly close to joining the Blues - could provide.
"And, to be fair, when we made the change, it didn't have straight away an impact.
"Because the players were still suffering from that anxiety.
"It's all down to them to change their mental attitude.
"They had more than time to score two goals or more.
"It was a reality that we just had a fantastic second half and we played in their half, created numerous opportunities, and we were dominant like we should've been in the first half."
There were also defensive errors from Chelsea, including from Alex, who has been quoted saying he could be interested in a move to Juventus.
Yossi Benayoun, who did not feature on Saturday, also tweeted in the evening that he expected to hear something about his own future on Wednesday.
Source: Team Talk
Source: Team Talk