Spurs fought from two goals down to earn a 2-2 draw at White Hart Lane but the two away goals gives the visitors the advantage going into the second leg of their quarter-final clash.
While Villas-Boas was full of praise for the Swiss outfit, he is certain that the Londoners can still go through.
"I think we limited the damage to give us the possibility of still getting through," said Villas-Boas told Sky Sports News. "Within all the negatives, there is the positive of still being in the tie and going away from home to try and get through.
"It wasn't a bad result, everyone has great belief we can go through.
"This Basel team was probably the best team I have ever seen at White Hart Lane. All the recognition goes to a top opponent who we had to play here tonight."
The return leg takes place in Switzerland on Thursday.