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The Blues were unable to fully capitalise on their chance to close the gap on the leading three, who all play on Sunday, after Fernando Torres fired another blank against a well-organised Canaries team who collected their first clean sheet of the season.
Chelsea are now 10 points behind leaders Manchester City, who host Tottenham this weekend, but having played a match more.
Villas-Boas said: "Bearing in mind Norwich's run of form, you could say it is not a bad point, but because we want to be champions, it puts in things in a different perspective ahead of tomorrow's fixtures.
"The games tomorrow can punish us hard in terms of what we were expecting. This could have been a good last opportunity for us to threaten for the title.
"The leaders can build a good margin tomorrow - that is the reality - but Arsenal must have a word to say, Tottenham the same.
"We don't know what will happen. We will have to wait and see if this is a point gained or two dropped."
Villas-Boas added: "We created enough opportunities to win the game, especially in the second half, but just could not find the back of the net.
"The players really fought hard, but we could not find it, either through our lack of efficiency or [Norwich goalkeeper] John Ruddy's performance.
"If we had done, then we would have taken all three points."
Torres has now not scored since October, and failed to find the back of the net for the 11th Premier League game.
The Spain striker got himself into good positions and was denied in the first half by a fine save from John Ruddy.
However, it turned out to be one of those afternoons when Torres somehow contrived to stab wide from eight yards on the hour, and he was eventually replaced by Belgian teenager Romelu Lukaku.
Villas-Boas, though, refused to point the finger of blame at the £50million man.
"Fernando tried really hard. His movement was sharp and effective. He also has a major impact in our offensive game and we were happy with his play," said the Chelsea boss, who elected not to include new signing Gary Cahill in the matchday squad.
"We cannot be hypocrites because in the last game against Sunderland everybody praised him for his form," the Portuguese added.
"He could not find the back of the net, but we are not just looking for that - we are looking for him to produce for the team and we had a good amount of chances to win."
Chelsea midfielder Frank Lampard went off in the first half with a calf injury, which Villas-Boas hopes will not keep the 33-year-old out of action for too long.
He said: "Frank will have to be assessed through an MRI scan, but the doctors tell us it is nothing very serious - maybe a muscle tear and we will have to find the extent of how long he will be out."
Norwich produced another composed display and created several chances of their own, with captain Grant Holt enjoying a running battle with the visitors' defence.
Manager Paul Lambert said: "We certainly gave as good as we got, especially in the first half.
"John Ruddy was excellent, but the whole group put their bodies on the line when they had to, and it was a huge point for us.
"When you are playing that level of a team, you have to keep your shape because otherwise they will pick you off."
The Canaries - who should next week complete a deal to sign Leeds captain Jonny Howson - are now well placed to mount a sustained bid to push on towards top-flight survival over the second half of the campaign.
Lambert added: "The lads are giving it a go every game and I will need everybody in the squad to hang in."
