Jan Vertonghen's 75th minute goal separated the two teams, allowing Spurs to move to fourth on the table, and Villas-Boas believed his side was deserving of a victory which brought about their second clean sheet in their past 10 outings.
"I think if there was one team to win this game it was us," he said.
"We were very patient and persistent in what we were doing and kept moving the ball well.
"We held on to the win. Obviously in this season we will continue to suffer goals in the last minute because football is unpredictable, but I think today the players showed the desire and ambition to put the wrong right and we managed to hang on to the result.
"We address it (conceding late goals) as a group in training by stimulating concentration in the last parts training. It is very difficult because you can't replicate the stress of a game and environment of a game.
"By increasing the complexity in terms of the exercises that you do, so the more complex the exercise the more concentrated you have to be, to do it you have to be very creative."