Spurs came unstuck at Emirates Stadium on Sunday, with Olivier Giroud grabbing what proved to be the only goal of the game.
A setback at the home of their arch-rivals saw Tottenham's perfect start to the season brought to an abrupt halt, but Villas-Boasa remains upbeat.
He told Sky Sports: "I think in the first half they had good chances, us as well.
"It was always a competitive game, with chances for both teams, but I think the game really changed in the second half. For Arsenal to finish with four full-backs means something to us and our domination.
"We kept on trying to get the equaliser. Drawing wasn't going to be enough, we wanted to win here, but they had the clinical ability in front of goal to score and then take the result.
"There was good determination there and I think, in the end, this can help you throughout the season. To expose Arsenal in this way in the second half sets a good example for us."
Villas-Boas, who confirmed afterwards that Gareth Bale is to complete a move to Real Madrid, concedes that his new-look side, which has been assembled at great expense, will take time to gel.
He added: "It's difficult because we haven't had time to do that.
"We played the Europa League game on Thursday night and again on Sunday. We are always recovering from the game before.
"We haven't had enough time at this moment to put the team together. The players did extremely well, just not enough to come away with something."
A disappointing day for Spurs also saw them lose Etienne Capoue to a second half knock, and the midfielder could be facing up to a lengthy spell on the sidelines.
Villas-Boas said: "He is being X-rayed now. He doesn't look too good. We will just have to wait for a bit more information."