Mr Howell added: "it shows we need a Government on our side, and this Government is not on our side".
Lord Rennard, chief executive of the Liberal Democrats, told Craig the result was an "abject humiliation" for the Labour Party.
Cameron hails by-election victory
Conservative leader David Cameron has hailed an "excellent result" in the Henley by-election, which saw Labour beaten into fifth place.
Mr Cameron said his party's win showed people were starting to think of the Tories as an alternative government.
But Gordon Brown - speaking a year after he became PM - said "by-elections come and by-elections go".
Labour lost its deposit with just 1,066 votes - fewer than the BNP, Greens, Lib Dems and Tory victor John Howell.
Mr Howell took the seat with 19,796 votes - a majority of 10,116 to the Lib Dem candidate - Stephen Kearney's 9,680.
He replaces Boris Johnson, who stepped down after becoming mayor of London.
'Disastrous result'
Mr Cameron said: "It's an absolutely excellent result in Henley" but a "disastrous result for the Labour Party".
And he said he believed it was "the first time in a long time when there's been a contest between the Conservatives and Liberal Democrats where there's been a swing to the Conservatives."
"I think what we saw was people who voted for all sorts of different parties, including the Liberal Democrats, now looking at the Conservatives and saying: 'Yes this is an alternative government that I can believe in'."
Both the Tories and the Liberal Democrats saw their share of the vote rise compared with the 2005 General Election while Labour's fell by more than 11%.
Giving his reaction to the result, Mr Brown, who is on a visit to Manchester, said: "By-elections come and by-elections go and of course we will listen to what people say."
'Higher petrol bills'
But he said his job was to improve public services and get the economy moving.
"I think people know that we are going through difficult times in the economy. It's my job to steer us through these difficult times," he said.
 |
RESULT AT-A-GLANCE
John Howell:
Conservative 19,796 Stephen Kearney:
Lib Dems 9,680 Mark Stevenson:
Green 1,321 Timothy Rait:
BNP 1,243 Richard McKenzie:
Labour 1,066 Chris Adams:
UKIP 843  |
"And people facing higher petrol bills, higher gas and electricity bills, people facing high food prices, it's my job to make sure I can do more to help people's standard of living improve."
Health Minister Ben Bradshaw admitted it was a "terrible result" for Labour but said it was down to current economic conditions rather than any unpopularity of Mr Brown.
"I don't believe he is personally unpopular," he added, saying that it was the "completely irrational" criticism by political commentators that was fuelling negative perceptions.
But Liberal Democrat leader Nick Clegg said the result showed Mr Brown's days in No 10 were numbered.
"Labour's days are well and truly over and it is the Liberal Democrats who are challenging the Conservatives in the south and Labour in the north," he said.
Meanwhile, a YouGov opinion poll for the Daily Telegraph suggests Labour has closed the gap on the Tories over the past month.
Labour was up five points on the month at 28% - still 18 points behind the Conservatives who dropped one point to 46%. The Liberal Democrats were down three on 15%.
But 61% of those surveyed thought Gordon Brown was a liability to the party, compared to 21% when he came to power a year ago.
Last year, 62% thought Labour would win the next general election, but that has dropped to 16% while 67% now think that the Conservatives are on course for victory, the poll suggests.
(Videos are available at the BBC site)
