Mr Osborne, who promised hope for an "aspiration nation" in his fourth budget to the Commons yesterday, told ITV1's Daybreak that he "wanted to be straight with the nation about the problems we face".
Referring to the current crisis in Cyprus, he said: "It's a difficult situation, but it could be a lot worse. You only have to watch your news bulletins to see other countries, not far from here, who have not confronted their problems and who are worried about getting money out of the bank.
"It's a difficult situation. It's a difficult neighbourhood.
"We have made a lot of mistakes as a country, over many years, building up these debts. But my determination is not to run away but to confront them head on."
Mr Osborne put his strongest emphasis yesterday on measures to encourage jobs, home-ownership and small businesses.
He brought a planned increase in income tax thresholds to £10,000 forward to 2014, which Tory aides said meant that everyone who paid the 10p tax rate under Labour will next year be taken out of the tax altogether.
Shadow chancellor Ed Balls said only the rich were better off following Mr Osborne's Budget.
He said: "He told us two years ago he would get the economy growing, get rising living standards and get the deficit down.
"Borrowing is up, the national debt is rising, the economy is absolutely flat and everybody in our country is worse off year by year, apart from the rich. It's not working."
Mr Osborne insisted the nation's economy was moving in the right direction.
"I've laid down a challenge to myself and this country," he told the programme. "We've got to confront those problems, not just shy away from them.
"But we're on the right track. It is a hard road, but we're getting there."
Mr Osborne said he wanted to help "hard-working families", adding that they would be in a better situation as a result of the Budget, with help to buy their own homes and to keep more of the money they earn.
"We're doing everything we can in very difficult times - which I don't excuse, people know these are difficult times - to help all those families who aspire to work hard and get on," he told hosts Aled Jones and Lorraine Kelly.
The Chancellor said he believed the economy would be improved as a result of the Budget, but admitted he knew he would be judged by its success.
"As a Government, we've come in and been confronted by these debt problems. It's very, very difficult, and of course we will be judged on whether we made the right call," he said.
"But my judgment was that when you're in a debt crisis, when your borrowing is high, if you deliberately seek to add to your borrowing, you're going to make the situation worse."
Other moves announced by Mr Osborne included knocking a penny of the price of a pint of beer and scrapping September's planned 3p rise in fuel duty.
Mr Osborne defended the move to increase the number of people applying for mortgages, but admitted: "If we were in a housing boom, we wouldn't be doing this."
The Chancellor told Daybreak: "We just want to help families, hard-working families, buy a home, put down a deposit and afford the mortgage."
He said there were many who could not afford a 20%-30% deposit on a house, but added: "I'm not talking about returning to the days of the 125% Northern Rock mortgages. I just want to help families, hard-working families."
Mr Balls told BBC Radio 4's Today programme the Chancellor's approach was not working.
"It is not really an approach at all at the moment," he said. "The deficit is hugely high and it is not changing."
He also questioned whether the housing guarantees would just drive up property prices.
"Unless the houses are there for people to actually go and buy this could lead to higher prices rather than jobs and growth in the housing market," Mr Balls said.
"It might work, but I fear it may not."