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 said.
"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."