"I understand and accept that the proposal I made was quite profound and intense," he said after voters narrowly rejected the sweeping constitutional reform by 51 percent to 49 percent.
Opposition activists were ecstatic as the results were announced shortly after midnight - with 88 percent of the vote counted, the trend was declared irreversible by elections council chief Tibisay Lucena.
Some shed tears. Others began chanting: "And now he's going away!"
Foes of the reform effort - including Roman Catholic leaders, press freedom groups, human rights groups and prominent business leaders - said it would have granted Chavez unchecked power and imperiled basic rights.
Chavez accepted the vote but claimed it was proof democracy is alive in Venezuela, led by a president not a dictator, reports CBS News correspondent Kelly Cobiella.
"From this moment on, let's be calm," he proposed, asking for no more street violence like the clashes that marred pre-vote protests. "There is no dictatorship here."
Chavez has used his country's position as the 4th largest supplier of oil to the United States to browbeat his best customer, and he has threatened a spike in prices, adds Cobiella.
Chavez, who was briefly ousted in a failed 2002 coup, blamed the loss on low turnout among the very supporters who re-elected him a year ago with 63 percent of the vote.
Seven in ten eligible voters cast ballots then. This time it was just 56 percent.
The defeated reform package would have created new types of communal property, let Chavez handpick local leaders under a redrawn political map and suspend civil liberties during extended states of emergency. Without the overhaul, Chavez will be barred from running again in 2012.
Other changes would have shortened the workday from eight hours to six, created a social security fund for millions of informal laborers and promoted communal councils where residents decide how to spend government funds.
Chavez's assuaging words - "don't be sad," he told supporters - didn't stop Nelly Hernandez, a 37-year-old street vendor, from crying as she wandered outside the presidential palace early Monday amid broken beer bottles as government workers took apart a stage mounted earlier for a victory fete.
"It's difficult to accept this, but Chavez has not abandoned us, he'll still be there for us," she said between sobs.
A close ally of Cuba's Fidel Castro, Chavez has redistributed more oil wealth than past Venezuelan leaders, and has also aided Latin American allies including Bolivia, Ecuador and Nicaragua that have followed Venezuela's turn to the left.
"He is a man who feels for the people, a man who has suffered, a man who comes from below," Carlos Orlando Vega, a 47-year-old carpenter's assistant, said outside a polling station in a Caracas slum on Sunday.
Vega is among tens of thousands of Venezuelans who, under Chavez, have new government-provided homes.
Chavez urged calm and restraint after his Sunday setback.
"I wouldn't have wanted that Pyrrhic victory," he said, suggesting a small margin wouldn't have been enough of a mandate.
Tensions surged in the weeks ahead of Sunday's vote, with university students leading protests and occasionally clashing with police and Chavista groups.
Chavez, 53, also suffered some high-profile defections by political allies, including former defense minister Gen. Raul Baduel.
Early Monday, Baduel reminded fellow Venezuelans that Chavez still wields special decree powers thanks to a pliant National Assembly packed with his supporters.
"These results can't be recognized as a victory," Baduel told reporters,
Baduel, who as defense minister helped Chavez turn back the 2002 putsch, said Venezuela can only be properly united by convening a popularly elected assembly to rewrite its constitution.
Chavez has progressively steamrollered a fractured opposition since he was first elected in 1998, and his allies now control most elected posts.
At opposition headquarters in an affluent east Caracas district, jubilant Chavez foes sang the national anthem.
"This reform was about democracy or totalitarian socialism, and democracy won," said opposition leader Leopoldo Lopez.
"At least now we have the guarantee that Chavez will leave power," said Valeria Aguirre, a 22-year-old student who had braved tear gas during street protests.
All was reported calm during Sunday's voting but 45 people were detained, most for committing ballot-related crimes like "destroying electoral materials," said Gen. Jesus Gonzalez, chief of a military command overseeing security.