Only an 87th-minute strike from Gylfi Sigurdsson saved Tottenham's skin as they had to settle for a point in Sunday's 2-2 stalemate with Everton at White Hart Lane.
The result means Spurs' destiny is no longer in their hands. They are now fourth in the table and should Arsenal win their game in hand against Everton on April 16, they will replace their bitter rivals in the top four with just six matches left.
Spurs have won just one game in their last six matches - a worrying sequence that has drawn comparisons with the club's dramatic collapse last term, when they won only five of their last 13.
Spurs paid a big price for that run as it cost them a place in the Champions League, and Villas-Boas does not want a repeat performance this season.
"Arsenal feel their belief is because they finish seasons very strongly and that belief helps them," the Spurs boss said.
"We don't look at ghosts in the past. We try to do our job properly. We want to win games. I think it could go down to the wire. It depends how many points we can get to the end of the season.
"At least with this break we can focus completely on the Basle game, and then we can recover for the Man City game, hopefully, with Bale, Lennon and Defoe. It depends how they react to treatment."