The draw meant no team had won a home fixture in the Premier League during the opening weekend of the campaign ahead of Manchester United's trip to West Brom and Villas-Boas did not get the start to his tenure as Chelsea boss he would have liked.
Terry believes Stoke wanted little more than a point from the game.
"They had made their intentions clear from the opening minutes," he told Sky Sports 1. "He (Villas-Boas) told us to just keep going and find the holes between the centre-halves."
The England skipper also feels Chelsea have the ability to regain the Premier League trophy this season.
He said: "We believe (we can win the league), our intention last season was to win it.
"We pushed Man Utd all the way and they have gone out and strengthened but we feel we have enough in the dressing room to go on and win the league."
Fernando Torres agreed with Terry that Stoke set out to defend and the result was always likely at a stadium where most teams struggle to break down the home side.
The ?50million striker said: "It is not easy to play against Stoke and this is only the first game of many we have to play and we have to start thinking about the next one. We are happy with the performance but not the result.
"We are disappointed with the result. We had some chances to score and two very clear penalty situations, but we had enough chances so it is no excuse.
"It is not a good result but it is a difficult stadium to play in and a difficult team to play against."
The former Liverpool frontman also stressed he was keen to move on from last season's disappointment, which saw him score only one goal after his big money move from Anfield in January.
"I was happy with my performance. A striker always likes to score but it is not always possible.
"I am only 27 and I haven't forgotten how to play and score, last season was a season to forget for me but it is in the past," he said.
Villas-Boas described the pushing and shoving by Stoke's players as "out of this world".
It was a frustrating debut for the 33-year-old Portuguese, who saw referee Mark Halsey turn down three concerted penalty appeals by Chelsea.
But it was the degree of physical contact in both boxes that vexed Villas-Boas.
He said: "A point I want to make when you are playing difficult games like this one is the amount of pushing and grabbing in the box, because it's out of this world.
"We are okay to deal with Stoke's set plays and we were competent enough to avoid the dangers they cause. We know the amount of goals they score with these set plays. But I think there's a limit to the pushing and grabbing, it makes it impossible."
Villas-Boas believes extra attention should be paid by referees to the issue and thinks the idea of additional officials is one that should be looked at.
He said: "Referees say these are the sort of details they are going to be aware of. It's difficult because they have to be aware of a number of situations but in this case maybe the referee needs some extra help.
"But there are no excuses because we were competent enough to defend those set plays, but it's a pity that it was happening."
The former Porto manager was not happy with the result but praised his side for the way they changed the game in the second half, and believes there are positive signs heading into the home matches against West Brom and Norwich.
Villas-Boas said: "I can't be pleased with a point but it's one of the most difficult grounds to play at. For our title challenge I would say one point at Stoke is not bad.
"It's not the greatest start to the Premier League of course, but we are happy we raised the level of the game in the second half.
"Unfortunately for us the goal didn't happen. We were close and we had the possession we wanted and we played in their half, the game looked more in our control, but I'm happy we were able to raise our level.
"It means against these kind of teams you are able to find space and create opportunities. Now we have to raise our game again for the two home games we have."
Stoke manager Tony Pulis was delighted to clinch a point.
"Of course it's a good point. We're delighted," he told Sky Sports News.
"First half we gave them a game, we were competitive and did some good things going forward.
"Second half we dropped off a little bit and Chelsea came into it."
Pulis reserved special praise for debutant Jonathan Woodgate, who he believes will be a force to be reckoned with when he hits his full potential.
He said: "He's going to be a good player. We're just oiling him at the moment, he's not really working at the top of his game. But you watch him today and I thought he was magnificent."
Despite the result being a disappointing one for Chelsea, Pulis believes they will still be fighting for the title come the end of the season.
"They're a great side. If you look at their substitutions they're bringing (Nicolas) Anelka, (Didier) Drogba and (Yossi) Benayoun off the bench," he said. "They've got great strength and depth and they'll be one of the top three teams this year without a question of a doubt."
Pulis admits Stoke are still working hard to strengthen before the transfer window closes on August 31.
"We're desperately keen to bring players in," he added. "We need four or five new faces in which will give us a little bit more quality and help us to progress.
"We've progressed very well as a football club and we have to take a step up and a step onwards. We have to do it at the right price for this football club and not put this football club at risk."
The Potters will be even more keen to bolster their resources after Matthew Etherington and Rory Delap both suffered injuries and were forced off early against the Blues.
Pulis said: "Matt has hurt his shoulder, which is disappointing for us. We don't know how bad that is.
"Rory just felt his hamstring again. We rested him, we didn't take him to Croatia (in the UEFA Europa League) the other day, we kept him back. But he's struggling again."
Source: Team Talk
Source: Team Talk