Third place would guarantee a place in the group stages of next season's Champions League while fourth would offer a play-off - the same route Tottenham used in their only previous foray into the competition two seasons ago.
Last season they finished fourth but were denied a chance to play in the Champions League this term because sixth-placed Chelsea took their place having lifted the trophy in Munich.
Tottenham had looked favourites to finish above Chelsea and Arsenal in third place until a few weeks ago, since when defeats by Liverpool and Fulham have halted their momentum.
They travel to Swansea City on Saturday in fourth place, one point behind Chelsea and four points above Arsenal, with both their London rivals having played a game less.
"Normally [to finish in the top four] requires in the 70-72 point margin," Villas-Boas told reporters on Thursday.
"70 is usually enough to be in the four spots. There are 24 points to be played for so that means we need 16 more points. You never know, but I think at this time we are within our objectives."
Arsenal recovered from a bigger points deficit last season to finish above Tottenham - and a home defeat by Fulham has left fans feeling jittery, especially as Arsenal's run-in looks easier than Tottenham's.
Villas-Boas denied that the players are emotionally scarred from last season's heartbreak.
"I don't think so," he said. "It's happened before but it doesn't mean it has to happen again.
"Circumstances are different, training is different, players are different so it doesn't have to happen again."
Tottenham skipper Michael Dawson, who was forced out of the England squad by injury, said Spurs need to get back to the kind of form that saw them go 12 league matches undefeated before going down 3-2 at Liverpool.
"We showed exactly what we're capable of when we went on that unbeaten run," he said. "We've got to look to do something similar between now and the end of the season. We know it will be tough, but the determination is there."
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