Los Angeles (CNN) Republican presidential candidates tore into CNBC's moderators at Wednesday night's GOP debate, issuing the sharpest attacks on the mainstream media of the 2016 election cycle.

Sen. Ted Cruz accused the moderators of trying to instigate a cage match, Sen. Marco Rubio called the media a super PAC for Hillary Clinton, and Donald Trump slammed the "ridiculous questions."

The candidates took to the airwaves again early Thursday morning and continued to rip CNBC for the tone and substance of the debate. And in the days ahead, sources said, campaign representatives will air their grievances to the Republican National Committee.

Ben Carson even told reporters Thursday that he would be demanding a new debate format.

‎"We need a change of format," Carson said during a press conference in Lakewood, Colorado. "Debates are supposed to be to 'get to know the candidates,' what is behind them. What it has turned into is a gotcha." ‎

Carson declined to specify what changes he would ask for, but said his campaign was reaching out to the other GOP candidates to "lay out a plan" going forward. The next Republican debate is on November 10, hosted by Fox Business.

The campaigns will find a sympathetic ear in RNC Chairman Reince Priebus, who blasted CNBC late Wednesday night for asking "gotcha" questions and said the network "should be ashamed."

"I was very disappointed in the moderators. I'm disappointed in CNBC," he told reporters in the spin room in Boulder, Colorado. "I thought they would bring forward a pretty fair forum here tonight. But I think it was one gotcha question, one personal low blow after another."

He continued, "It's like they tried to design a Rubik's cube for every question to take the worst element, I think, of what the moderators and what the media should bring to the table. And all I can tell you is that while I'm pretty much proud of our candidates for pretty much sticking together, I'm very disappointed in the moderators and I'm very disappointed with CNBC."

Priebus went even further in an official statement: "One of the great things about our party is that we are able to have a dynamic exchange about which solutions will secure a prosperous future, and I will fight to ensure future debates allow for a more robust exchange," he wrote. "CNBC should be ashamed of how this debate was handled."

The candidates' attacks on the media were red meat for the conservative base, which already has a deep mistrust of the mainstream press. But even by conservative standards, the candidates' broadsides on Wednesday night were aggressive and unrelenting, and delighted the audience in Boulder.

The candidates' fierce criticism of CNBC -- the first sustained volley against the media of the current campaign -- immediately called to mind the frequent attacks against the press during debates in the 2012 elections.

Brian Steel, CNBC's senior vice president for public relations, stood by the moderators' performance.

"People who want to be President of the United States should be able to answer tough questions," he said in a statement late Wednesday night.

Yet the morning after the debate on Thursday, GOP candidates continued to criticize CNBC and the mainstream media generally. In an interview with CNN's Chris Cuomo on "New Day," Rubio took issue with the tone and substance of the debate and said he hoped future debates would do a better job of focusing on important issues.

Carly Fiorina, appearing on "New Day" with Alisyn Camertoa, chided the "liberal media" and The Washington Post specifically for continuing to focus on her remarks about Planned Parenthood.

Later in the show, New Jersey Governor Chris Christie told Camerota that he was going to keep standing up to debate moderators. "I'm not going to allow them to ask stupid questions," he said.

The campaigns will further address their frustrations in a conference call with the RNC in the days ahead, campaign sources said. Their goal is to ensure that the Fox Business debate on November 10 focuses on more substantive issues, skips the "gotcha" questions, and provides all candidates with more equal speaking times.

On Wednesday night, CNBC's moderators struggled to maintain control of a debate that, according to many journalists on Twitter, they appeared ill-equipped to handle. The panelists, usually familiar with covering Wall Street and finance, were left scrambling to talk about a presidential race they seemed to know little about.

At one point during the debate, Jeb Bush campaign manager Danny Diaz began pounding on the control room door, shouting at the CNBC producers about how the network wasn't giving equal time to all the candidates, a source with a rival campaign told CNN.

The night left GOP hopefuls and reporters wishing for the previous Republican debate moderators from Fox News and CNN.

Politico's John Bresnahan joked that CNBC was frantically calling CNN and Fox "to ask how to run a debate," while Matthew Continetti, the editor of the conservative Washington Free Beacon, wrote: "Winners of GOP Debate so far: Jake Tapper and Anderson Cooper."

On stage, Cruz was the night's most vocal media critic, condemning CNBC for trying to instigate fights between the candidates while ignoring issues that mattered to voters.

"The questions that have been asked so far in this debate illustrate why the American people don't trust the media," Cruz said, after being asked about the debt ceiling. "This is not a cage match."

"How about talking about the substantive issues people care about," Cruz added to thunderous applause from the audience.

The audience in Boulder was electrified by Cruz's attack. Social media mentions of Cruz blew up during his attack on the media -- it was the top moment on Facebook, the social network said -- while pollster Frank Luntz said his focus group "burst out in applause at Ted Cruz's media attack."

"Ted Cruz's focus group dials [hit] 98 with his attack on media bias," Luntz wrote on Twitter. "That's the highest score we've ever measured. EVER."

The Texas Senator wasn't the only one to slam the mainstream media at the debate: Rubio, asked to respond to a Florida Sun Sentinel editorial that had called on him to drop out of the race, charged that it "evidence of the bias that exists in the American media."

Later in the debate, Rubio declared that the mainstream media was so biased in favor of Clinton that it was effectively functioning as her Super PAC.

Trump, who had predicted before the start that the debate would be "unfair," criticized CNBC's moderators for asking "ridiculous questions," and later called a question posed to Mike Huckabee "nasty."

New Jersey Gov. Chris Christie looked one moderator in the eye and said, "Even in New Jersey what you're doing is called rude."

At various points in the debate, both Rubio and Trump accused the moderators of having their facts wrong.

CNBC's problems were further compounded by the network's meandering commentary between the night's two debates, which was widely panned on Twitter.

"CNBC does underscore that the only people sometimes more vapid than candidates are journalists talking about candidates," New York Times columnist Nicholas Kristof tweeted, echoing the sentiments of many journalists and political operatives.

"Is this a public access channel?" asked Jon Favreau, the former speechwriter for President Barack Obama.