He said Americans "aren't looking for more spin; they're looking for honest answers".
Obama had once led comfortably in the state's opinion polls but gave up some ground in recent weeks to Clinton.
But on Tuesday he called attention to claims by the Clinton campaign that the North Carolina race would be a "game-changer."
"Today, what North Carolina decided is that the only game that needs changing is the one in Washington, DC," he said.
Answering charges that he was having trouble winning in big states that will be important in the general election, Obama characterised his North Carolina win as "a victory in a big state, a swing state, and a state where we will compete to win if I am the Democratic nominee for president of the United States".
North Carolina is the 10th largest US state by population.
Earlier on Tuesday, Obama was asked about the difficulty he has had in connecting with working-class voters, particularly white men, in states in the industrial Midwest like Indiana that will be important in the fall elections.
|Democrats are concerned about a protracted |
battle between Clinton and Obama [AFP]
"There've been some states where we have won the blue-collar vote: Wisconsin. We won it in Iowa. We won it in Minnesota.
"Then there are other states where we've not done so well, mainly because people are much more familiar with Senator Clinton and President [Bill] Clinton and their track record."
"You have to give them credit. They're the best established brand name in Democratic politics, maybe in politics overall. They've been on the scene for 20 years. They're not going to go down easy."
Only six state contests remain, but the 16-month battle between Clinton and Obama has raised concerns in the Democratic party that it will appear disunited to voters ahead of the November general elections.
In his North Carolina victory speech, Obama acknowledged there were "bruised feelings on both sides".
"Each side desperately wants their candidate to win."
Still, he said, "this fall, we intend to march forward as one Democratic Party, united by a common vision for this country".