The visitors were frustrated for large parts of their trip to South Wales as they found Cardiff goalkeeper David Marshall in fine form.
The 28-year-old denied Roberto Soldado on numerous occasions, while also thwarting Christian Eriksen and Gylfi Sigurdsson.
However, there was nothing he could do about Paulinho's late winner, as the Brazilian flicked home substitute Erik Lamela's pass.
And Villas-Boas believed that was the least his side deserved for their dominance.
"Today it was different from normal in that there was justice in football," said the Tottenham boss. "We created so many chances that there could only be one winner.
"It's a great win. But I suffered a lot…like everyone else!
"Bearing in mind the win they got against Man City there won't be many teams getting points here, so I'm happy."
Late goals were a feature of Tottenham's performances last season and Villas-Boas was delighted to see another game decided with a stoppage-time winner.
"It's persistence, the more they come (late goals), the more the players believe they can do it," he added.
"We kept the ball moving well, (but) they kept on resisting - the sense of frustration was building in the team
"It was a great contribution from Erik (Lamela) in that goal, all of them made the right impact and that's the spirit you need."
