"And where is the moral compass in allowing a campaign of lies and half truths about your opponents?"
He said the "historic" by-election was "only the second time a Conservative victory has been had in a Labour seat in the last 27 years".
"I think it shows that people want change in our country," he added.
The Tories say if the vote share results were repeated across the country at a general election, the Conservatives would have a majority of 190.
The by-election was triggered by popular Labour MP Ian Gibson quitting after he was barred from standing again for the party over his expenses - sparking anger among some constituents.
The Lib Dems came third with 4,803, narrowly ahead of UKIP on 4,068, who enjoyed their best ever by-election result.
Liberal Democrat leader Nick Clegg said the result was bad for Labour and hailed an "excellent campaign" by his party's candidate, April Pond.
"Gordon Brown's growing failure as prime minister and his ham-fisted treatment of a popular MP have resulted in disaster for Labour," he said.
Mr Brown acknowledged it was "clearly a disappointing result" for Labour but people should consider what was happening in the constituency.
"The voters were clearly torn between their anger and dismay at what's been happening with MPs' expenses, something we have been trying to clean up and at the same time support for the former MP, the Labour MP Ian Gibson, who was very popular.
"I don't think any party can take a great deal of cheer from this, the Conservative vote went down, the Liberal vote when down - only the fringe parties saw their votes going up."
UKIP spokesman David Campbell Bannerman said it was a "great result" for them which he said showed them as a "serious and credible alternative to the three old parties".
"A lot of our support has come from Labour voters, not just Tories ... UKIP is growing, we are capable of taking votes from a number of parties and from those who don't vote normally as well," he told the BBC News channel.
The Greens - who are the main opposition party on the local council - were pushed into fifth on 3,350, although it was also their best by-election result ever.
Green candidate Rupert Read said: "The Norwich North campaign was done on a fraction of the budget of the large parties, some of which deluged residents with countless leaflets. We are pleased to have done so well without that kind of overkill."
Gordon Brown: 'I don't think any party can take a great deal of cheer from this'
Ms Smith, who at 27 will be the youngest MP in the House of Commons, paid tribute to Dr Gibson in her victory speech and wished her Labour rival Mr Ostrowski a speedy recovery - he was hospitalised with suspected swine flu days earlier.
She will not take her seat officially until October, after the summer recess, but said she would be concentrating on her constituents.
"This isn't about me jumping off here and then going and living up on expenses for the three summer months," she said.
"This is about getting down to it, being honest, and being held to that. If I can be a very very good constituency MP and a very very good local representative for people here, then I hope they'll continue to put their trust in me and I hope I can serve them well."
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