"Gov. Romney may dance around his positions but if you want to be president, you owe the American people the truth," Obama said at a post-debate rally.
Romney's campaign dismissed the criticism as "damage control."
Obama's aggressive stand came as his campaign conceded he will have to adjust his debate style. Wednesday's night event was widely viewed as a win for Romney and a lost opportunity for Obama to connect with the American people as national polls had showed him with a slight advantage heading into their first debate.
Obama said that when he reached the debate stage "I met this very spirited fellow who claimed to be Mitt Romney. But it couldn't have been Mitt Romney," Obama said, adding that the "real Mitt Romney has been running around the country for the last year promising $5 trillion in tax cuts that favor the wealthy. The fellow on stage last night said he didn't know anything about that."
The president also accused Romney of misrepresenting past statements on education and outsourcing. In tough comments, the president said Romney "does not want to be held accountable ... because he knows full well that we don't want what he's selling."
Obama panned Romney's suggestion during the debate that one way to pare back federal spending is to cut the subsidy for PBS, which airs "Sesame Street." Romney said he likes PBS and "I love Big Bird," but said the country couldn't afford to keep borrowing money from China to pay for things like that.
"When he was asked what he'd actually do to cut the deficit and reduce spending, he said he'd eliminate funding for public television. That was his answer. I mean thank goodness somebody is finally getting tough on Big Bird. It's about time," Obama joked. "We didn't know that Big Bird was driving the federal deficit. But that's what we heard last night. How about that? Elmo, too?"
Romney campaign spokesman Ryan Williams responded to the accusations of dishonesty by saying Romney demonstrated in the debate why he should be president.
"In full damage-control mode, President Obama today offered no defense of his record and no vision for the future," Williams said. "Rather than a plan to fix our economy, President Obama simply offered more false attacks and renewed his call for job-killing tax hikes."
In a conference call with reporters, Obama senior adviser David Axelrod said the president would make "adjustments" and would need to determine by the next presidential debate on Oct. 16 in Hempstead, N.Y., how best to counter what the campaign considers Romney's evasions on a series of issues.
Comparing it to a playoff game in sports, Axelrod said: "You evaluate after every contest and you make adjustments and I'm sure that we will make adjustments. I don't see us adding huge amounts of additional prep times. There are some strategic judgments that have to be made and we'll make them."
Axelrod sought to turn the questions about the debate into a matter of character, repeatedly accusing Romney of "hiding the truth and the facts" from the American people.
"It was a very vigorous performance, but one that was devoid of honesty," Axelrod said of Romney. He said the Republican presidential nominee offered well-delivered but "fraudulent" lines that will be hard to hold up over the remainder of the campaign.
Building on that narrative, Obama's campaign quickly released an ad questioning Romney's truthfulness, arguing that he didn't level with middle-class families on how his tax plan would affect them. "If we can't trust him here, how could we ever trust him here?" the ad says. It was airing in Colorado, Florida, Iowa, New Hampshire, Nevada, Ohio and Virginia.