The Tottenham striker has been in lethal form so far this season, and currently leads the scoring charts at White Hart Lane after starting all but one of the club's league games
The England striker has started 16 of Spurs' 17 Premier League games so far this campaign, scoring nine goals and taking them to fourth in the table.
"The new manager has come in and he has shown great faith in me," the 30-year-old said.
"He said to me from the beginning, 'I want you to stay at the club, I know you will score goals'. It has been fantastic. I have got my chances, I have scored goals.
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"I just want to keep it going, keep scoring more goals and help the team achieve something this year."
Despite the side's impressive attacking performances, Defoe admits that they have to improve the defensive side of their game after Villas-Boas held a meeting regarding the side's issue with conceding late goals.
Spurs have conceded 10 goals in the final 15 minutes of games, a joint-high with bottom-of-the-table Reading.
He continued: "There is no point standing here telling you what was said in the meeting because I would be standing for a long time.
"But it is not just the defenders - it's the whole team. It's that famous saying: defend from the front.
"It is something that has happened and is something that we do
Defoe has recently paired up with Emmanuel Adebayor after playing alone for much of the season due to the Togo man's injury problems.
The former Arsenal man could be in line to represent his country at the Africa Cup of Nations next month, but Defoe would rather he stayed at White Hart Lane.
The England international said: "Obviously, for us, we want him to stay here and help us to win games.
"At the end of the day, I can't stand here and say he shouldn't go because it is special when you play for your country.
"It is a decision that Ade has to make himself."