The Portuguese manager called for calm and renewed concentration at White Hart Lane after Spurs moved seven points clear of their north London rivals on Sunday afternoon
First-half goals from Gareth Bale and Aaron Lennon ensured the home side went into half-time ahead and, despite Per Mertesacker scoring early in the second period, Spurs held on to win the game and consolidate their place in the top four, moving seven points clear of their rivals in the process.
Tottenham built a similar lead over their neighbours last season before being overhauled and pipped to third place, and Villas-Boas is using that scenario as a warning to anyone who may be getting complacent at White Hart Lane.
“There's still so much to go,” the Portuguese told Sky Sports. “Last year by this time Arsenal made up the seven-point difference to Tottenham and we know how it finished at the end of the season.
“Obviously the motivations are different. We are extremely confident, they are on a low at the moment. For them to be able to jump back is going to be very difficult but they can do it against [Swansea] City. We just have to continue our job.”
The win at White Hart Lane meant Tottenham leaped to third in the Premier League, two points above London rivals Chelsea, and two behind second-placed Manchester City - however City have a game in hand, against Aston Villa on Monday night.
Villas-Boas admitted the win was important for the fans and for the battle for Champions League qualification, but says there is still plenty of football to be played.
“[The result is] very important for what it means but nothing is finished yet,” the 35-year-old said.
“We still have to fight hard. Arsenal now have to play Swansea City and we play Liverpool so it could be another big weekend for us.
“We'll try to profit from another important fixture and keep doing our job. It's important to get the most amount of points as we can to try and finish where we want to be.”