Villas-Boas told the club's official website that he is pleased with side's performance as they remained patient to break Villa down.
He said: "Extremely happy in both first and second half. There was immense dedication from the players and we have an important win.
"It was a very difficult game but we were superior. We knew scoring first would make the difference. We had a lot of chances.
"Overall a great performance. We told the players at half-time to persist with the intensity and we would come good."
A fourth successive league win for Spurs improves their record with 14 points from 7 matches in the Premier League and takes them to fifth in the table.