"The results are very severe," Aso said. "There has been a deep dissatisfaction with our party."
Unemployment and deflation - and an aging, shrinking population - have left families fearful of what the future holds.
Fed up with the LDP, voters turned overwhelmingly to the opposition Democratic Party of Japan, which ran a populist-leaning platform with plans for cash handouts to families with children and expanding the social safety net.
"This is a victory for the people," said Yukio Hatoyama, leader of the Democrats and almost certainly Japan's next prime minister. "We want to build a new government that hears the voices of the nation."
Hatoyama and his party - an eclectic mix of former Liberal Democrats, socialists and progressives - face a daunting array of challenges, economic and demographic.
Japan's economy has been hit hard amid the global recession and falling demand for its exports. The unemployment rate has spiked to a record 5.7 percent and younger workers have watched the promise of lifetime employment fade. Incomes are stagnant and families have cut spending.
The country also faces threats as its population ages, which means more people are on pensions and there is a shrinking pool of taxpayers to support them and other government programs.
The Democrats' plan to give families 26,000 yen ($275) a month per child through junior high is meant to ease parenting costs and encourage more women have babies. Japan's population of 127.6 million peaked in 2006, and is expected to fall below 100 million by the middle of the century.
The Democrats are also proposing toll-free highways, free high schools, income support for farmers, monthly allowances for job seekers in training, a higher minimum wage and tax cuts. The estimated bill comes to 16.8 trillion yen ($179 billion) if fully implemented starting in fiscal year 2013 - and critics say that will only further bloat Japan's already massive public debt.
In foreign relations, the Democrats have said they want Tokyo to be more independent from Washington on diplomatic issues, though they have stressed that the U.S. will remain Japan's key ally and that they want to keep relations good, while also strengthening ties with their Asian neighbors.
Official results were to be announced midmorning Monday, but media exit polls indicated the Democrats would win 300 or more of the 480 seats in the more powerful lower house of Japan's parliament. That would be enough to give them the power to establish a new Cabinet and name Hatoyama as prime minister by the end of next month.
The LDP was seen winning about 100 seats - a third of its strength before the vote.
"It's a historic election in that a clear alternation of power has happened for the first time in the postwar period," said Koichi Nakano, professor of political science at Sophia University in Tokyo. "It's kind of hard to know whether this is going to lead to a real change in policy, at least for the short term."
The loss was only the second the Liberal Democratic Party - traditionally the champion of big business and conservative interests - has suffered since it was founded in 1955. The only other time it was out of power was for less than 11 months in 1993-1994, and that was to a coalition of eight parties that quickly collapsed.
The LDP had survived through previous recessions in Japan but since then families have grown less secure about the future.
With only two weeks of official campaigning that focused mainly on broad-stroke appeals rather than specific policies, many analysts said the elections were not so much about issues as voters' general desire for something new after more than a half century under the LDP.
"All the bad things over the last 54 years finally caught up to them," said Fumio Morita, 45, who runs a bar in Tokyo. "It's good that they are no longer in power."
Japan has had three prime ministers in three years, all of whom were deeply unpopular for their perceived lack of leadership and for failing to get the country out of its deepening economic morass.
The LDP tried to fight back by reminding voters that their party led the nation out of the ashes of World War II. They also argued that the Democrats, who have never run the government, were irresponsible and inept.
Hatoyama's party, which already controls the upper house with two allies, held just 112 seats in the lower house before parliament was dissolved in July.
The Democratic Party needed to win a simple majority of 241 seats in the lower house to ensure it could name the next prime minister. The 300-plus level would allow it and its two smaller allies the two-thirds majority they need in the lower house to pass bills.
AP reporters Mari Yamaguchi, Kelly Olsen, Shino Yuasa and Tomoko Hosaka contributed to this report.