Fifth-placed Spurs twice came from behind to draw 2-2 at Stamford Bridge, but their fate is no longer in their own hands ahead of matches with Stoke and Sunderland.
Villas-Boas' side are one point behind Arsenal and three behind Chelsea and have a far inferior goal difference to their London rivals.
"The destiny's not in our hands any more," the Portuguese said.
"What we have to do is what we had to do also, to win the next fixtures and hopefully see if somebody can slip up and change our position.
"Hopefully if we're able to take this to the last game of the season, when we play at home [against Sunderland], and Arsenal go to Newcastle and Chelsea play Everton, anything can happen. It's unpredictable."
Villas-Boas expects the next round of fixtures - Chelsea's match at Aston Villa on Saturday, Spurs' Sunday contest with Stoke and Arsenal's Tuesday clash with FA Cup finalists Wigan - could determine the top-four battle.
"This next fixture is decisive for everybody," he added.
"Arsenal has had this whole time to rest [since playing at QPR last Saturday]. It won't be an advantage for Wigan to play after an FA Cup final so early, but that's the reality.
"Chelsea have a difficult game at Villa, we have an extremely difficult game against Stoke. I think anything can happen.
"[But] we don't depend on ourselves any more.
"We did ever so well to get a point in a difficult situation.
"I'm extremely pleased by the performance. The reality is that we have to do our job and hopefully something can happen.
"For all of the determination and ambition we've shown this season, hopefully we can be rewarded at the end of it by qualifying."
Chelsea must wait to secure their Champions League return after being pegged back twice by Spurs.
Oscar and Ramires, either side of an exquisite Emmanuel Adebayor shot, gave the hosts a half-time lead, before substitute Gylfi Sigurdsson struck in the 80th minute to deny Chelsea a seventh successive Premier League home win.
Chelsea interim boss Rafael Benitez was frustrated by his side's failure to net a third and end the match as a contest and lamented the defensive failings which contributed to Spurs' equalisers.
Adebayor appeared to be marginally offside in the build up to Sigurdsson's strike and Benitez felt fatigue played a part, particularly out wide where Spurs enjoyed supremacy in the latter stages.
"We had the chances on counter attacks to score the third goal and finish the game," Benitez said.
"It was an open game. We were in control and we didn't win.
"Adebayor was offside, but still we have to defend a little bit better.
"The tempo of the game was too high. It was massive for both teams.
"We didn't have legs. We had players that were tired, especially in the wide areas. We had a problem with the [Spurs] full-backs going forward."
Benitez's decision to introduce Yossi Benayoun late on was an unpopular one among fans, particularly with Frank Lampard unused on the bench.
The Spaniard defended the substitution.
"We were weak in the wide areas," Benitez said.
"We needed to be strong. I didn't see any other wingers on the bench. He was the only one I had."
Chelsea's defenders also backed off to allow Adebayor to equalise in the first half.
"We could do better, not give the ball away," Benitez said.
"We gave them too much time and space to decide. That is my concern."
Villas-Boas praised the contribution of Adebayor in a match he described as one of the games of the season.
"Adebayor's performance was absolutely outstanding," the Spurs boss said.
"He's been struggling with knee pain and he put himself forward for the team with a great game and a great performance."
It was Villas-Boas' first return to Stamford Bridge since his sacking 14 months ago.
"Great reception," he said. "I was open to any kind of reception to be fair.
"[It was a] great respect from the Chelsea players and the Chelsea fans, a good game and a good spectacle."