On Saturday, the former President while speaking at a fundraising forum in Washington cautioned the candidates against pursuing polices that were not "rooted in reality", the BBC reported on Monday.
Obama, who was in office from 2009 to 2017, said "ordinary Americans" didn't want to "completely tear down the system".
The remarks represented Obama's most pointed intervention yet in a crowded race featuring 18 candidates.
Although none of the Democratic candidates explicitly rebuked Obama's comments, Vermont Senator Bernie Sanders mounted the strongest defence of his policy platform.
Replying to questions on a forum aired by Univision, a Spanish-language TV network, he was asked whether the former President was "right" to say voters didn't want systemic change.
Sanders said: "Well, it depends on what you mean by tear down the system."
"The agenda that we have is an agenda supported by the vast majority of working people," he said, adding: "When I talk about raising the minimum wage to a living wage, I'm not tearing down the system. We're fighting for justice."
Meanwhile, Massachusetts Elizabeth Warren struck a more conciliatory tone, choosing to praise Obama's trademark health care policy, the Affordable Care Act.
"I so admire what President Obama did," Warren said at a campaign event in Iowa.
"He is the one who led the way on health care and got health care coverage for tens of millions of Americans when nobody thought that was possible."
New Jersey Senator Cory Booker said the party ought to be focusing its energy on defeating President Donald Trump, not internal political squabbles, reports the BBC.
Julian Castro, a former mayor of San Antonio, Texas, said he was confident any Democratic candidate would beat President Trump, regardless of their political persuasion.
The Democratic race is still in flux as the first of the state-by-state votes that will decide which of the contenders challenges Trump for the White House looms in Iowa in February 2020.
Pete Buttigieg, mayor of South Bend, Indiana, topped the latest poll of likely Democratic voters in Iowa.
The latest polling suggests that former Vice President Joe Biden and Warren were the front-runners, while Sanders and Buttigieg were not far behind.
( With inputs from IANS )