"It is the majority," he said. "There is a majority that won, and there is a minority that we recognize and respect, even though many of them hate us."
Capriles stressed that Maduro must also recognize the political will of the millions of voters who supported the opposition.
"Here there is no majority," he said. "There are two halves."
Sunday's closely watched election comes at a time of political polarization and uncertainty for Venezuela. It was the second time in just over six months that voters in the South American country cast ballots in a presidential vote.
Chavez, who ruled Venezuela for 14 years, celebrated a triumphant re-election victory in October. After his death on March 5, authorities announced new elections to select his successor.
'I am not Chavez, but I am his son'
Maduro, 50, has been Venezuela's interim leader since Chavez's death. When he registered to run for the presidency last month, he told supporters, "I am not Chavez, but I am his son."
They weren't blood relations, but in one of his last public appearances, Chavez tapped Maduro as his replacement.
"My firm opinion, as clear as the full moon -- irrevocable, absolute, total -- is ... that you elect Nicolas Maduro as president," Chavez said in December, waving a copy of the Venezuelan Constitution as he spoke. "I ask this of you from my heart. He is one of the young leaders with the greatest ability to continue, if I cannot."
It was the first time Chavez had named a successor.
His comments dramatically changed the political landscape and became the basis for Maduro's push to ascend to the presidency after his mentor's death.
Throughout the campaign, Maduro pledged to continue Chavez's efforts to build "21st century socialism" and said his platform consisted of following the former president's plan for the country.
At rallies for Maduro, a recording of Chavez's voice belting out the national anthem boomed through loudspeakers.
At one campaign event, he told supporters that Chavez appeared to him in the form of a little bird to give him spiritual support.
And Maduro's official campaign theme song began with a militant drumbeat and Chavez's voice, endorsing his candidacy.
Campaigns bracing for a battle
Capriles, 40, said he was pushing a more moderate approach, promising to continue social programs and improve the country's economy.
The opposition candidate lost to Chavez in October's presidential vote, but he came within 10 percentage points of the longtime leader. It was a significant gap, but the closest any opposition candidate ever came to defeating Chavez during his rule.
More than 78% of the 18.9 million Venezuelans registered voted in Sunday's presidential election, Lucena said.
In Venezuela, elections officials said Sunday evening that the day had proceeded smoothly without major incidents.