The Chancellor said the coalition was determined to stick by its plan for economic recovery after the rating was lowered by a notch to AA1.
The credit rating agency warned late on Friday that "subdued" growth prospects and a "high and rising debt burden" were weighing on the economy.
Shadow chancellor Ed Balls called the downgrade "a humiliating blow" to the Prime Minister and Chancellor, who he said "must urgently take action to kick-start our flatlining economy".
But Mr Osborne said the loss of the gold-plated status did not mean the Government should change course.
"We have a stark reminder of the debt problems facing our country - and the clearest possible warning to anyone who thinks we can run away from dealing with those problems," he said.
"Far from weakening our resolve to deliver our economic recovery plan, this decision redoubles it.
"We will go on delivering the plan that has cut the deficit by a quarter, and given us record low interest rates and record numbers of jobs."
Mr Osborne went on: "As the rating agency says, Britain faces huge challenges at home from the debts built up over many, many years, and it is made no easier by the very weak economic situation in Europe.
"Crucially for families and businesses, they say that 'the UK's creditworthiness remains extremely high' thanks in part to a 'strong track record of fiscal consolidation' and our 'political will'.
"They also make it absolutely clear that they could downgrade the UK's credit rating further in the event of 'reduced political commitment to fiscal consolidation'.
"We are not going to run away from our problems, we are going to overcome them."
The downgrade is a major blow for Mr Osborne, who has been coming under increasing pressure to take action to stimulate the economy.
The Chancellor has used maintaining the top credit rating for Government bonds as one of the key arguments for the Government's austerity programme.
However, Labour has insisted that withdrawing demand from the economy has put it more at risk by stunting growth.
The statement from Moody's highlights the problems the weak medium-term economic outlook poses for deficit reduction plans.
It now expects the "period of sluggish growth" to "extend into the second half of the decade".
"The main driver underpinning Moody's decision to downgrade the UK's Government bond rating to AA1 is the increasing clarity that, despite considerable structural economic strengths, the UK's economic growth will remain sluggish over the next few years due to the anticipated slow growth of the global economy and the drag on the UK economy from the ongoing domestic public- and private-sector deleveraging process," the agency said.
"Moody's says that the country's current economic recovery has already proven to be significantly slower - and believes that it will likely remain so - compared with the recovery observed after previous recessions, such as those of the 1970s, early 1980s and early 1990s."
Mr Balls said: "This credit rating downgrade is a humiliating blow to a Prime Minister and Chancellor who said keeping our AAA rating was the test of their economic and political credibility.
"It would be a big mistake to get carried away with what Moody's or any other credit rating agency says.
"Tonight's verdict does not change the fact that the credit rating agencies have made major misjudgements over recent years, not least in giving top ratings to US sub-prime mortgages before the global financial crash.
"But what matters is the economic reality that the credit rating agencies are responding to. Moody's themselves say the main driver of their decision is the weak growth in Britain's economy.
"Their judgment is in response to nearly three years of stagnation, a double-dip recession, billions more borrowing as confirmed this week and broken fiscal rules. This is why the Chancellor is fast running out of credibility."
Mr Balls went on: "The issue is no longer whether this Chancellor can admit his mistakes but whether the Prime Minister can now see that, with UK economic policy so badly downgraded in every sense, things have got to change.
"In the Budget the Government must urgently take action to kick-start our flatlining economy and realise that we need growth to get the deficit down.
"If David Cameron and George Osborne fail to do so and put political pride above the national economic interest we face more long-term damage and pain for businesses and families."