Spurs broke their transfer record to acquire Roberto Soldado from Valencia, and the Spain international provided an instant return on that investment with a debut goal.
Soldado held his nerve from the penalty spot to break Palace's stubborn resistance, with Tottenham unable to turn possession into clear-cut opportunities.
Villas-Boas was, however, pleased to get the 2013/14 campaign off to a winning start and believes there will be more to come from his side once they have gelled together.
He told Sky Sports: "We spoke before the game how difficult it would be because of the surprise factor.
"Ian (Holloway) put his team together very well because he had three players very narrow just behind the striker, which we weren't expecting. That caused a bit of unpredictability and it was a tough game.
"We had some good chances to put the game to bed but, bearing in mind 90 minutes, I think we deserved to win.
"Naturally, the team dropped a little bit after the goal. We had some chances on the counter, which could have put it to bed and it would have been game over. We always had that edge to our game. The overall performance was excellent and we had some chances."
Villas-Boas, who confirmed there has been no movement in Real Madrid's protracted pursuit of Gareth Bale, added on debutants Soldado, Paulinho, Nacer Chadli and Etienne Capoue: "It was important for the new signings. They have just been mentioning the intensity of the Premier League. For them it was the first time and it was a bit of a surprise. I think they did extremely well.
"The objective is always to make your team stronger than the year before, that is our goal and objective in the market. We will keep trying to do that.
"I think the team has developed a lot. Hopefully we have the range of options that enables us to always come with quality."