Chavez said later that Venezuelans may not yet be ready for his proposed constitutional revisions.
"Did Hugo Chavez choose the wrong timing? It could be. It could be that we aren't mature enough," he told state television late on Monday.
"Before searching for guilty ones, I have to say that I could have made a mistake in my selection of a time to make the proposal."
Earlier on Monday, he had said that by conceding defeat he had proved that, unlike past Venezuelan governments, he respected the will of the people.
He publicly congratulated the opposition and urged restraint from both sides.
"I ask all of you to go home, know how to handle your victory," he said. "You won it. I wouldn't have wanted that Pyrrhic victory."
The narrow margin was the first victory for an emboldened opposition against Chavez after nine years of electoral defeats and Al Jazeera's Latin America editor, Lucia Newman, said it was elated.
The loss was also attributed to traditional supporters
who abstained from Sunday's vote [Reuters]
Adolfo Taylhardat, an opposition politician, told Al Jazeera the result was "a victory for Venezuelan democracy".
"We have defeated president Chavez's intention to change the type of state we are living in," he said.
"He wanted to turn Venezuela from a democracy to a socialist state in which he would have almost full power."
Students, rights groups, business lobbies, opposition parties, the Roman Catholic Church and former political allies all lined up against Chavez, calling the proposed changes authoritarian.
Even Chavez's usually loyal ex-wife voted against his reforms.
Tensions had surged in recent weeks as university students led protests and occasionally clashed with police and pro-Chavez supporters.
George Ciccariello, a Venezuela watcher with the University of California at Berkeley in the US, told Al Jazeera there had been "a great deal of disinformation" about Chavez's campaign prior to the vote.
"There were rumours, there was pamphleteering, there was printing false copies of the reform proposal.
"That said though, Chavez really took a hit on this in terms of his moderate supporters not turning up to vote."
A Chavez victory would have meant:
Two-term presidential limit abolished to allow him to keep contesting polls
Him taking control of country's erstwhile autonomous central bank
Work day cut from eight hours to six
Voting age lowered from 18 to 16
Social security benefits extended to informal workers
Al Jazeera's Newman said diehard "Chavistas" were calling those who did not turn up to vote "traitors", but many traditional Chavez voters felt their president had gone too far with his proposed reforms and stayed away.
Chavez supporters were left shell-shocked by the result but marched to the presidential palace on Monday, vowing to somehow push through the rejected reforms.
Newman said it was pre-mature to say that Chavez had lost the leadership or power.
She said he was still very powerful and popular, and even without the constitutional overhaul, already has far-reaching powers to reshape the government, the economy and society.