The Portuguese boss, after several fine saves by Spurs keeper Brad Friedel had kept the game goalless, saw his side take the lead when Mousa Dembele, signed from Fulham this week, scored on his debut in the 68th minute.
But, as happened in their draw with West Bromwich Albion seven days ago, Spurs conceded a late equaliser when Robert Snodgrass scored from close range five minutes from time.
And Villas-Boas's day got worse when substitute Tom Huddlestone, only on for seven minutes, was shown a straight red card for a challenge on Jonny Howson.
Gareth Bale was also booked for dissent shortly after as Tottenham lost their composure.
This result will only increase the pressure on Villas-Boas, dismissed by Chelsea last season before Spurs' London rivals won the Champions League, and the home fans let him know it at the final whistle by greeting their team with a chorus of boos.
"You have to accept their disappointment," said the coach. "It has not been the ideal start to the season, but it doesn't mean that we haven't been working hard to get the wins that our fans want. We had two good games, Newcastle and West Brom, that we didn't win.
"We have to work on our sharpness and concentration to make sure it doesn't happen again."
On the opposite touchline was a feeling of optimism. "What impressed me was that we never dropped," said Chris Hughton, the Norwich manager. "We were always looking for an equaliser."
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