The Portuguese coach recognised the Potters' efforts as Spurs peppered the opposition goal with shots throughout, while Tony Pulis singled out Asmir Begovic for a fine display
The hosts registered 21 shots on goal with 14 on target, but were unable to find a way past the Potters with Asmir Begovic in fine form for the visitors.
And the Portuguese coach admitted the opposition's "extremely physical" performance proved key to preventing his side from picking up a much-needed victory in their race for a top four place.
"I want to be extremely positive because the players tried really hard, it was not going to be easy," he told reporters.
"Stoke are on an unbeaten run for a reason and I think they proved it once again today. Extremely competitive, extremely physical, difficult to break down, good organisation, tremendous energy and power, and it was never easy for us.
"To our credit, we had a couple of chances, but we couldn't find the goal that would unlock them and bring them out. So as the time increased it was ever more difficult to get the goal."
The draw, along with Everton's comeback win over West Ham, saw Spurs drop out of the top four on goal difference.
The north London side are now level on points with local rivals Arsenal, West Brom and new fourth-spot occupiers Everton ahead of the busy festive period, and Villas-Boas feels any further slip-ups will be pounced upon in future.
He continued: "There's four teams level on 30 points, so [the draw] doesn't make any difference. The table is very, very tight and on a weekend everything can change, and I think changed this weekend.
"Obviously we wanted to win, but it's not a bad performance, the players gave everything."
Stoke boss Tony Pulis also hailed his side's defence, namely goalkeeper Asmir Begovic for keeping his concentration late on as both Mousa Dembele and Gylfi Sigurdsson went close as the game entered stoppage time.
"We're pleased with the first half, thought we played really well first half, we restricted Tottenham to just a few chances," Pulis said.
"In the second half they put us under pressure and we're indebted to Asmir for making a great save.
"Tottenham are a fantastic club, they've got players who can hurt you. So many players that, within a couple of seconds, can change the game.
"It's always a nervous place to come in lots of respects. But we're very, very pleased that we came away with something," he added.