The Swiss club skipped away to a two-goal lead in North London before Spurs fought back for a 2-2 draw in the quarter-final first leg and Villas-Boas is aware his side has an enormous task on their hands for the return bout at St Jakob-Park next week.
"I think we limited the damage to give us the possibility of still getting through," he said.
"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 plays with great belief we can go through. This Basle team was probably the best team I have ever seen at White Hart Lane. All the recognition goes to a top opponent we had to play here tonight."