Gylfi Sigurdsson struck three minutes from time to grab a point for Spurs at White Hart Lane after poor defending had allowed Phil Jagielka and Kevin Mirallas to put the Toffees ahead following Emmanuel Adebayor's first-minute strike. Tottenham struggled without Gareth Bale and Aaron Lennon, but it was in defence that Villas-Boas will have most concerns.
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, saying: "The positive aspect is we've been in this position, chasing, before."
He added: "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."
Registering a draw at White Hart Lane without the suspended Marouane Fellaini and Steven Pienaar would ordinarily be seen as a good result, but Moyes was disappointed that his team failed to take all three points.
With Everton now six points off Spurs, Moyes admits his hopes of leading his team back in to the Champions League are very slim.
He said: "We're playing a good team and we've taken four points from Spurs this season. It's not a bad performance, but does it help us?
"Probably not. We're hanging in there. I knew if we won we could get right in the mix. I'm pleased with a point because Spurs played well. I thought we did as well, in patches.
"In truth, maybe we should have just about nicked it at the end. I think Tottenham can cope with their losses more than we can. We don't have the squad to cope with that loss (of Fellaini and Pienaar)."
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- Aaron Lennon