The sitting lawmaker Ian Gibson last month quit after revelations that he claimed nearly 80,000 pounds (93,000 euros, 132,000 dollars) in second home expenses on a London flat which he later sold cheaply to his daughter.
Brown admitted it was "clearly a disappointing result" but said voters were disaffected with all main parties in the wake of the expenses furore.
"I don't think any party can take a great deal of cheer from this," he added.
Although it comes as little surprise, the defeat shows Brown's government facing a struggle to beat David Cameron's Conservatives -- who are well ahead in opinion polls -- at a general election which must be held within a year.
Cameron said the Conservative victory showed people had "had enough" of Brown and "want change in our country."
But despite the poor result, it seems unlikely that Brown will face a fresh leadership challenge in its wake.
It was his first by-election test since an abortive threat to his premiership as a wave of ministers resigned amid dire European Parliament and English local election results last month.
That was the second time Brown's premiership has faced a possible challenge since he took over from Tony Blair in June 2007.
Foreign Secretary David Miliband -- reportedly linked to the first failed plot last year -- said that the by-election result "is not evidence for the need of a change in the Labour leadership."
But commentators say Norwich North highlights the badly weakened state of Labour, which has been in power since 1997.
"It is hard to recall a recent by-election in a supposedly safe Labour seat about which the party has seemed more fatalistic," The Guardian newspaper said Friday.
"Under Gordon Brown, Labour has become a party that no longer expects to win."
The poll in the historic university city of Norwich was the first triggered by the expenses scandal which has seen dozens of lawmakers announce they will step down, and House of Commons speaker Michael Martin resigning.
Many local Labour activists were outraged by the party's treatment of Gibson, who quit after he was barred by Labour from standing at the next general election.
Some lawmakers claim he was made a scapegoat by the party for the wider expenses scandal
Charles Clarke, the Norwich South Labour lawmaker and ex-cabinet minister, said Gibson was forced out by a "kangaroo court" while left-winger lawmaker Alan Simpson claimed he was "the victim of a political assassination orchestrated by the party machine in London."
Simpson said: "The machine wanted a sacrificial victim and who better than to go for one of Gordon's critics rather than his friends?"
Chloe Smith, the victorious Conservative candidate, is only 27 years old. She will be the youngest lawmaker in the House of Commons when she takes her seat when parliament returns from its summer recess in October.
She described her win as a "victory for honest politics."
The Labour candidate, Chris Ostrowski, was handicapped by suspected swine flu which saw him hospitalised Tuesday. He did not attend the count. Turnout in the poll was around 45 percent.
Under Brown, Labour had already suffered heartland by-election defeats to contrasting foes -- notably to the Conservatives, who won Crewe and Nantwich in northwest England last year, and to the Scottish National Party, which holds devolved power north of the border, and who won in Glasgow East.
The by-election in ex-speaker Martin's Glasgow North East seat is likely to be held in November.
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Brown admitted it was "clearly a disappointing result" but said voters were disaffected with all main parties in the wake of the expenses furore.
"I don't think any party can take a great deal of cheer from this," he added.
Although it comes as little surprise, the defeat shows Brown's government facing a struggle to beat David Cameron's Conservatives -- who are well ahead in opinion polls -- at a general election which must be held within a year.
Cameron said the Conservative victory showed people had "had enough" of Brown and "want change in our country."
But despite the poor result, it seems unlikely that Brown will face a fresh leadership challenge in its wake.
It was his first by-election test since an abortive threat to his premiership as a wave of ministers resigned amid dire European Parliament and English local election results last month.
That was the second time Brown's premiership has faced a possible challenge since he took over from Tony Blair in June 2007.
Foreign Secretary David Miliband -- reportedly linked to the first failed plot last year -- said that the by-election result "is not evidence for the need of a change in the Labour leadership."
But commentators say Norwich North highlights the badly weakened state of Labour, which has been in power since 1997.
"It is hard to recall a recent by-election in a supposedly safe Labour seat about which the party has seemed more fatalistic," The Guardian newspaper said Friday.
"Under Gordon Brown, Labour has become a party that no longer expects to win."
The poll in the historic university city of Norwich was the first triggered by the expenses scandal which has seen dozens of lawmakers announce they will step down, and House of Commons speaker Michael Martin resigning.
Many local Labour activists were outraged by the party's treatment of Gibson, who quit after he was barred by Labour from standing at the next general election.
Some lawmakers claim he was made a scapegoat by the party for the wider expenses scandal
Charles Clarke, the Norwich South Labour lawmaker and ex-cabinet minister, said Gibson was forced out by a "kangaroo court" while left-winger lawmaker Alan Simpson claimed he was "the victim of a political assassination orchestrated by the party machine in London."
Simpson said: "The machine wanted a sacrificial victim and who better than to go for one of Gordon's critics rather than his friends?"
Chloe Smith, the victorious Conservative candidate, is only 27 years old. She will be the youngest lawmaker in the House of Commons when she takes her seat when parliament returns from its summer recess in October.
She described her win as a "victory for honest politics."
The Labour candidate, Chris Ostrowski, was handicapped by suspected swine flu which saw him hospitalised Tuesday. He did not attend the count. Turnout in the poll was around 45 percent.
Under Brown, Labour had already suffered heartland by-election defeats to contrasting foes -- notably to the Conservatives, who won Crewe and Nantwich in northwest England last year, and to the Scottish National Party, which holds devolved power north of the border, and who won in Glasgow East.
The by-election in ex-speaker Martin's Glasgow North East seat is likely to be held in November.
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