Spurs dominated large portions of the encounter but needed an injury-time winner from Paulinho to edge the Bluebirds 1-0.
Despite the victory coming in the 93rd minute, Villas-Boas was confident that Tottenham's performance warranted a victory.
"There could only be one winner," said Villas-Boas.
"We played so much football it would have been unfair to leave here with only one point.
"We got our reward in the end, but with the chances we created, if it wasn't for (goalkeeper David) Marshall, it could have been a more comfortable game.
"You worry it can be one of those games. We played so open and sometimes on the counter they had a chance. But today, more than maybe any other game, we deserved the win.
"It's satisfying as I don't see many teams coming here and winning against a team who are well organised and well managed."