Spurs overcame a tardy start to move up to fifth on the table thanks to goals from Andros Townsend (31st minute) and Roberto Soldado (69th) and Villas-Boas felt his players did well to combat Villa's long-ball style of game to control proceedings in the second half.
"It was difficult in the first minutes," Villas-Boas told Sky Sports. "It was very unpredictable because Villa kept putting some very long balls in behind us, so they kept stretching us.
"We had to put our act together and I think we did after the 20th minute. We got hold of the ball and started creating things.
"In the second half, we were really, really good. After we reached 2-0, we could have gone on to score more.
"After the setback, particularly at home (3-0 loss to West Ham), we have to respond and I think we did it in a good fashion to keep ourselves in touch with the top.
"I think we deserved the result. We want to build on from here and continue to gather the most amount of points as possible."
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