Spurs raced into a 2-0 lead in the first half but were overrun after the interval and were clinging on at the end.
"A draw would have maybe been fairer, I have to agree with that," Villas-Boas admitted. "But sometimes it's important to get three points like this by fighting.
"The 2-0 advantage gave us a bit of extra confidence and we made a couple of mistakes because of that extra confidence."
Villas-Boas was clearly unhappy with the timing of the fixture, adding: "All the teams are very tired and we are on a continuous run from the Europa League and two Premier League fixtures where we've used most of the same team.
"Most of the other teams haven't done so, they are fresher than us.
"This is an important result given this is a midweek fixture when most of the teams have dropped points and we have gained some."
Gareth Bale made one goal and scored the other for Spurs and Villas-Boas admitted some of the big clubs would be chasing him, adding: "Tottenham want to keep him here as long as we can but we understand players like this have propositions, have market which is the nature of the game."