Gareth Bale and Aaron Lennon scored in Sunday's North London derby at White Hart Lane as Spurs moved back into third place and opened up a seven-point lead over fifth-placed Arsenal.
Both teams have tricky games still to play this season and Villas-Boas knows that Tottenham's win over Arsenal will mean little if they do not push on and remain consistent.
"It was very, very important for what it means, but obviously nothing is finished yet," he told Sky Sports.
"We have to believe that we still have to fight hard. We have to play Liverpool (next weekend) and we have to try to profit from another important fixture and keep doing our job.
"It is important we gather as many points as we can to finish where we want to be."
Arsenal finished strongly last season to pip Tottenham to third, with Chelsea's Champions League triumph ensuring Spurs missed out on this season's competition.
"Last year, by this time, Arsenal made the difference of seven points to Tottenham and we know how it finished," Villas-Boas added.
"Motivations are now different. We are extremely confident. They are on a low at the moment.
"We have to continue to do our job."
Given that Spurs have a difficult run-in, which includes a trip to Stamford Bridge, Villas-Boas last night played down the idea that his men could finish third and above his former employers.
"It's extremely difficult," Villas-Boas said. "The margin is very, very slim for them, we hope we can (stay above them), but it will be extremely difficult.
"We have seen so many shifts in league position recently towards the end of the season, particularly among the big teams involved in Europe, so you can't really stop.
"You just have to continue. Confidence makes a difference. It's not a big enough margin yet for us to be completely safe.
"Obviously we will approach the Liverpool game (on Sunday) with extreme care, they are on a good run too and play excellent football too."
Emmanuel Adebayor and Mousa Dembele had to come off yesterday, but Villas-Boas believes both will be fit for Thursday's Europa League game against Inter Milan.
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