He said: "It's going to go down to the wire and things as it stands with Arsenal, Everton, Chelsea and Tottenham all in the frame for that Champions League qualification.
"In games like this you can really see how much desire is in both teams to get those objectives."
"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.
"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."
Their game with Everton was played on Sunday due to Spurs' ongoing participation in the Europa League and Villas-Boas was happy with his side's effort after a grueling 2-2 draw against Basle on Thursday night.
"I think it was a good game, full of opportunities for both sides, a really competitive match," he added.
"We wanted to win so obviously we're not pleased but bearing in mind the circumstances, bearing in mind our super effort on Thursday it's good to see the team react once again.
"We left it late which didn't give us a chance to go on for the third but I think that their second goal comes a little bit against the run of play because we started the second half very very well.
"But credit to an Everton side which battled their way through and played for an entertaining game."
This was the first time that Spurs had not started with both Lennon and Bale in their first XI since November 2009. The success they have achieved ever since has been based on the pace, delivery and goals of both players.
Tottenham felt their absence strongly today. Sigurdsson provided the crucial equaliser and Lewis Holtby offered energy, but neither of the two, and the returning Clint Dempsey, threatened Tim Howard for much of the game.
A tense atmosphere did not help matters either, with the home fans all too aware of the importance of the fixture to the club's Champions League dreams after two years in the Europa League.
"I don't think we relaxed," the Spurs boss added.
"You give Everton a small amount of space and they punish you.
"It was an entertaining game of football.
"I think it was a good performance by the team, individually and collectively, although it was not the result that we wanted."