The win, which the manager dedicated to Alex Carroll, one of the club's football administrators whose mother passed away in the days leading up to the match, moves Spurs up to fourth in the Premier League.
"We wish him the best to recover for his great loss," Villas-Boas told reporters of the Spurs employee before going on to speak glowingly of a performance that he compared to their 3-2 win at Manchester United in September.
"It was a good first half, we kept the ball well and managed to create lots of opportunities," the Portuguese observed. "We always looked in control of the game.
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"It was very similar to Old Trafford, where we had an extremely good first half but in the second half we showed that desire to defend and hold onto the result."
Saints, buoyed by Jay Rodriguez's goal, pressured heavily in the second period and, questioned whether he was pleased with the number of blocks his defence put in, Villas-Boas noted: "When the nature of the game changes, it is that kind of effort you want from your players.
"Suddenly they have been immense. Once again we came back late from our trip against Maribor, arrived at 02.00GMT and had two days to recover to play a game like this, one that requires a big physical effort.
"It is important for the fans and this win is a massive win for the players. For them to be embracing the Europa League the way they are. One of our best performances was against Villa at home after we arrived at 04.00GMT from Greece.
"It is such a good win for them and we benefit from the big games being played in the Premier League. We want to be there at the top and make the most of the fixtures against Southampton and Wigan before Man City and Arsenal."
Villas-Boas also reserved praise for Gareth Bale, who scored Tottenham's opener in what was the first game he had played against the club with whom he began his career.
"I am extremely happy for him," the Spurs boss enthused. "He's a massive player for the team, someone who in the small opportunities can make the difference.
"He defended well, scored, and it was good for him to get back on the score sheet and certainly someone we rate very very highly."
For opposite number Nigel Adkins, it was another game that got away but he remained defiant, stating: "The message before the game was to get up and get at them. We have young players who are learning, improving all the time.
"We gave it a good go and the introduction of Emmanuel Mayuka was a good one. The supporters got behind the players and we dominated the second half."
Despite defeat leaving the Saints winless in four games, Adkins remained positive over his own future. Asked whether he felt he would be given time to succeed, he said: "Yes. You need to be positive about what you're doing and everyone's working hard for each other."