The visiting Londoners controlled large parts of the first half at Goodison Park, but Everton responded positively after the restart.
Ultimately, neither side were able to find the back of the net, but rather than be disappointed, Villas-Boas believes that his players claimed an "important" share of the spoils.
"It was very tight, a good game, we had good moments and a great first half with pressing and good attacking combinations and we should have gone ahead in the first half," he told BBC Sport.
"The second half evened itself out and in the last 30 minutes they had a go at us. We still managed to slot in a couple of situations in the second half. The result is fair and with a bit more luck we could have gone ahead in the first half.
"Good point in the end. We could have gone second but, considering Everton's aspirations, it was important to get a point."
Next up for Spurs is a Europa League tie against Sheriff Tiraspol on Thursday evening.