Tottenham would have moved ahead of Chelsea into third had they won but they ended the afternoon in fifth after their north London neighbours and Everton recorded victories against Wigan and West Ham respectively.
Villas-Boas' men threw everything at the Potters but they could not find their way through a defence the Tottenham boss had described as one of the best in Europe during the week.
The Staffordshire side showed exactly why they have the best defensive record in the league as Robert Huth, Ryan Shawcross and Asmir Begovic all put in towering performances to keep the likes of Jermain Defoe, Gareth Bale and Emmanuel Adebayor at bay.
Villas-Boas, whose side face Aston Villa on Boxing Day, was not happy at seeing his team slip below Arsenal on goal difference.
"No-one enjoys being level on points with Arsenal at this club," Villas-Boas said.
"I have experienced this rivalry for the first time this year and I have spoken very highly about it before.
"It is an extremely healthy competition between both teams but we have to continue now.
"It was a difficult game. Stoke are an extremely competitive and physical team who are difficult to break down.
"I want to be extremely positive as the players really tried hard."
- Sports & Recreation
- Ryan Shawcross
- Asmir Begovic
- Robert Huth