Gylfi Sigurdsson struck three minutes from time to grab a point for Spurs who struggled without the scoring talents of Gareth Bale and the creative wizardry of Aaron Lennon, but it was in defence that Villas-Boas will have most concerns.
The Spurs back four, who shipped two soft goals to Basle on Thursday, allowed Phil Jagielka enough space for the defender to nod Everton level while Kevin Mirallas had little trouble gliding past Scott Parker and Steven Caulker before beating Hugo Lloris to make it 2-1.
The result means Spurs' destiny is no longer in their hands. They are now third 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.
But having been outside of the Champions League places for most of the season Villas-Boas still has faith his team can qualify.
"The positive aspect is we've been in this position, chasing, before," said Villas-Boas, whose side are not in action next weekend when Arsenal host Norwich.
"Arsenal feel their belief is because they finish seasons very strongly and that belief helps them.
"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 (Jermain) Defoe. It depends how they react to treatment."