Chelsea took the lead through Oscar before Emmanuel Adebayor equalized with a tremendous strike, but Ramires re-established the one-goal margin until Gylfi Sigurdsson rescued a point for Spurs with 10 minutes to play.
The result means that with two matches left to play, Chelsea remains in third place with 69 points, two ahead of Arsenal and three in front of Spurs, meaning Villas-Boas’s side must now rely on other teams if it is to finish in the top four.
He told Sky Sports: “Obviously with a point we don't depend on ourselves any more, people have to drop points, but our focus is on doing our job in the remaining fixtures and in the Premier League anything can happen, so let's keep the faith.
“We wanted to win obviously, [but] the feeling is that a point is not bad. Our focus will be to do our job and with the teams that Arsenal and Chelsea have to play, us too, fighting for survival, hopefully something can happen.
“The Premier League is completely unpredictable. Wigan have to go to Arsenal, Chelsea have a difficult game against Villa on Saturday. We have a difficult game against Stoke who are also fighting. These next fixtures before the emotions of the final day of the season can be decisive.”
The first half saw Chelsea generally control the match and the hosts took a 2-1 lead into the break, but Villas-Boas believes his side reacted well in the second period as Chelsea became more aggressive.
“It was good for us to get back into the game," he continued. "In the second half we increased the tempo and played really, really well. It was difficult to control all of Chelsea's creativity, but we had great determination at 2-1 to hold on to their attacking strength and create our own chances.
“Chelsea became very, very aggressive in the second half so that's why we thought of strengthening our midfield. We put Sig [Sigurdsson] on the left coming inside and then [Clint] Dempsey on to increase our options in the middle to link up with Adebayor.
“With that I think we managed in the last 20 minutes to avoid Chelsea's pressure, started finding a lot more spaces and had the control of the last 20 minutes, but Chelsea on the counter looked extremely dangerous.”
Villas-Boas went on to praise his two goalscorers as he endorsed Adebayor’s selection as Man of the Match before highlighting Sigurdsson’s persistence at getting into good positions this season despite luck rarely going his way.
“[They were] great goals,” he said. “Ade's [Adebayor] first goal is absolutely unbelievable, for him to score in such a decisive place. He had a great great game, [and] really linked up the game well for us and we saw that finishing touch that he has. I think he was a fully deserved man of the match.
“Gylfi [Sigurdsson] did ever so well. He gets into these goalscoring positions a lot. He's been extremely unlucky this season because he's been in deadly positions before, [but] he hit the post and hit the bar, but today it was a deadly finish.”