Spurs won 2-0 thanks to goals from Andros Townsend and Roberto Soldado.
The result lifted the Londoners to fifth in the Barclays Premier League and was the perfect response after a shock 3-0 loss to West Ham last time out.
Villas-Boas said: "It was difficult in the first minutes to get hold of the ball because Villa kept putting long balls behind us.
"When we managed to get more control, from the 20th minute onwards, we managed to score and the goal gave us the confidence to play our game.
"In the second half that really showed, in a better way. We started playing much better, lots of attacking options.
"I think 2-0 is what we deserved."
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