Spurs, whose sale of Gareth Bale to Real Madrid was confirmed on Sunday evening, went down to Olivier Giroud's first-half goal, which left them with no goals from open play in their opening three Premier League games.
Villas-Boas said: "It was always a competitive game with chances to both teams, but I think the game really changed in the second half.
"I think for Arsenal to finish with four full-backs means something to us, to our domination that we kept on trying to get the equaliser and obviously drawing was never going to be enough we wanted to win here.
"But I think they had that clinical ability in front of goal to score and then to take the result through so in the end it's a good win for them.
"It showed great spirit from the players to approach the game in such a courageous way in the second half, there was some good determination there so in the end this can help you through the season.
"To expose Arsenal in this way in the second half is such a good example for us."