Spurs have made a habit of conceding late goals this season - including two in last weekend's 2-1 defeat at Everton - but they were able to keep a clean sheet after Jan Vertonghen had put them ahead in the 75th minute.
Villas-Boas said: "It was a good, good win and I think we deserved to win today. We did everything right today. We had so many chances, so many opportunities to put the game to bed even earlier.
"We concentrated, we were responsible and it would have been very unfair if we had not won today.
"Swansea made it very difficult. Not only are they strong in attack, but their defence is very organised. It was difficult to break them down and we had to be patient.
"We were doing everything right in the first half and in the second half. It was a tremendous effort from the boys and I think they got the reward for their patience.
"You just have to be persistent. We kept the ball well, moved the ball well and fortunately enough through a set-play we managed to get the goal.
"You saw the players acknowledge the fact that we have been suffering and showing great commitment to finish the game.
"Obviously the season is long and we will continue to suffer goals in the last minute, that is the nature of the game. But we acknowledge the mistakes we made at Everton and today we did it well."
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