Spurs beat Dinamo Tbilisi 3-0 at White Hart Lane on Thursday to advance with an 8-0 aggregate win into the group stages.
Despite possessing a 5-0 lead going into the match, Villas-Boas is pleased with the attitude of his Premier League outfit.
"We couldn't be complacent. All the boys did extremely well," Villas-Boas told reporters.
"After a 5-0 win you can come into the game with a laid back attitude. They didn't. They kept their professionalism and got some chances and got some good moments of football with some good combinations."
Spurs face Arsenal at the Emirates Stadium on Sunday.