Fifth-placed Spurs twice came from behind to draw 2-2 at Stamford Bridge on Wednesday night and now sit one point behind Arsenal and three behind Chelsea entering the final two games of the campaign.
Spurs also have a far inferior goal difference to their rivals, but Villas-Boas hopes his side's efforts result in a place among Europe's elite.
"For all of the determination and ambition we've showed this season, hopefully we can be rewarded at the end of it by qualifying," Villas-Boas said.
The Spurs boss recognises his side must rely on slip-ups and believes 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. The reality is that we have to do our job and hopefully something can happen."