Obama's remarks came after a secretly taped and newly released video of the Republican presidential nominee showed Romney describing "47 percent of the people" as Obama supporters who depend on government and believe they are victims.
"My expectation is that if you want to be president, you have to work for everyone, not just for some," Obama said in a taping of the "Late Show" with David Letterman.
It was Obama's first response to the Romney video, which roiled Romney's campaign and put him on the defensive about his views about nearly half the nation.
In the video, taken during a May fundraiser and posted online Monday, Romney said it is not his job "to worry about those people." He was referring to what he called Obama's locked-in supporters who believe they are "entitled to health care, to food, to housing, to you name it."
Romney has since said he made his point inelegantly in trying to describe differing visions for the nation.
"There are not a lot of people out there who think they are victims" or simply entitled, Obama said.
Obama also said he did not know what Romney was even referring to with his "47 percent reference."
The president said that when he won in 2008, 47 percent was the amount of voters who went for his opponent, Republican Sen. John McCain. McCain actually got about 46 percent of the popular vote.
Current polling shows Obama with a slight edge over Romney.
"One thing I've learned as president," Obama said, "is that you represent the entire country."
Obama said people understand that the presidential candidates will make mistakes on the campaign trail. He said that includes one he regrets from 2008, when audio from one of his own private fundraisers had him saying that some residents of depressed rural areas get bitter and "cling to guns or religion or antipathy to people who aren't like them."
Having said that, Obama added: "What I think people want to be sure of is you are not writing off big chunks of the country."
The president appeared on the TV show before a night of fundraising in New York City.