First-half goals from Gareth Bale and Clint Dempsey secured the points as Tottenham withstood an impressive second-half fightback from Saints.
With Spurs having played in the Europa League on Thursday night, Villas-Boas is pleased with how his squad are coping with the busy schedule.
"We have been struggling with a lot of injuries and that's why these players have been immense so far," Villas-Boas told Sky Sports.
"We don't have the in-depth squad that other teams have. We're playing Thursdays and Sundays, having two or three days to recover and that's why the feeling is extra special."
Villas-Boas acknowledged Spurs were given a test by Southampton and felt a third goal after half-time would have finished the game off.
He added: "It was a great win for us, particularly on a weekend when most of the top teams played each other.
"We showed our technical ability in the first half and our desire in the second half to take the result. It was an important win for us.
"At half-time we spoke about scoring the third goal and they put us on the back foot a little bit. It was a solid performance from us.
"They came up very, very strong and we knew only the 3-0 would put the game to bed. It was certainly difficult for us and we're happy with the win."