It was their second fightback in four days after Spurs had come back from two goals down to draw with Basel in the Europa League on Thursday, and Villas-Boas is pleased with his side's never-say-die attitude.
"I think it was a good game, full of opportunities for both sides, a really competitive match," Villas-Boas told Sky Sports News. "We wanted to win so obviously we're not pleased but bearing in mind the circumstances, bearing in mind our super effort on Thursday it's good to see the team react once again.
"We left it late which didn't give us a chance to go on for the third but I think that their second goal comes a little bit against the run of play because we started the second half very, very well.
"But credit to an Everton side which battled their way through and played for an entertaining game."
Spurs are currently fourth in the Premier League table, two points ahead of rivals Arsenal in fifth.