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Sen. Barack Obama, the newly minted presumed Democratic presidential nominee, said Wednesday that it was "very humbling" to be the the first African-American to lead a major party's ticket and expressed confidence the party would unify behind him.

"You think about all the people who had to knock down barriers for me to walk through this door," he said. "And the challenges they went through were so much more difficult, so much more severe, and the risks they took were so much greater that I will say, last night standing in that auditorium, it struck me that it was testimony to them."

The senator from Illinois also said his successful campaign for the Democratic presidential nomination has taught America's children that the Oval Office is within anyone's reach.

"I have heard from a number of people already, both black and white, that their kids -- 7, 8, 9 years old -- take for granted now that, of course, a black can run for president, that a woman can run for president," he said. "There is a matter-of-factness to it that I think bodes well for the future." Listen to Obama call his victory 'humbling'

Asked whether he was disappointed that his rival for the Democratic nomination, Sen. Hillary Clinton, did not concede outright Tuesday night, Obama said his priority was unifying the party. Read full article »

CNN Candy Crowley, Roland Martin and Ted Barrett contributed to this report.

All About U.S. Presidential Election • Democratic Party • Hillary Clinton • Barack Obama