The Hill reports Chaffetz said Crowley overstepped her role during the debate while Crowley defended herself.
"When you have two candidates disagreeing, it's not the role of the moderator to say, 'Mr. President, you're right' or 'Gov. Romney, you're right,' " he said to Crowley during a roundtable on CNN's "Starting Point." He added that he thought she did a great job as moderator other than during the exchange on Libya.
"It wasn't necessarily your place to try to be fact-checker right there," Chaffetz said. "I happen to think that your assessment of that was wrong, and so I was a bit frustrated on that particular point."
Crowley explained to CNN after the debate that she thought Romney "was right in the main, I just think he picked the wrong word."
She explained further in Wednesday morning's interview: "There is no question that the administration is quite vulnerable on this topic, that they did take weeks to go, 'Well, actually there really wasn't a protest and actually it didn't have anything to do with the tape.' That took a long time."
"Then we got hung up on this 'Yes, he said'; 'No, I didn't'; 'I said terror'; 'You didn't say terror.' There was this point where they both kind of looked at me," Crowley explained of the exchange. "What I wanted to do was kind of move this along."