Spurs went into Sunday's game at the Etihad Stadium with the best defensive record in the Premier League, but Jesus Navas and Sergio Aguero both scored twice for City.
Navas' first goal came after just 15 seconds and Spurs boss Villas-Boas was left to reflect on where things went wrong for his team.
"It was a difficult start," Villas-Boas told Sky Sports.
"Obviously conceding a goal in 15 seconds puts your plan in doubt and everything that you've been preparing. It's difficult to take.
"We had a very, very good reaction to the goal we conceded, and that's probably the only positive of the game that we have.
"Everything went bad for us. From being one of the best defences in the country to conceding six goals, there's not a lot we can say.
"We can say City were excellent, but we were extremely poor today and we paid a heavy price."
Spurs have now failed to score in their last three Premier League games, and only bottom two Crystal Palace and Sunderland have scored fewer times this season.
Villas-Boas' side again lacked a cutting edge and the Spurs boss will look for solutions ahead of Thursday's Europa League tie away to Tromso.
He added: "The good thing is that, in the Premier League or in a top club, there's always another game coming and another possibility to bounce back.
"We have a game on Thursday where we have to show that we are present, we are there and to continue to do our job.
"We have to see now the mistakes we made and reflect a little bit.
"We've created so many chances before, and it's an ongoing conversation we have to make sure we have to finish up the chances.
"The team is capable of creating, it's not finishing which is the situation right now."