Members of the Democratic Party had criticized Buttigieg for appearing on Fox News, but Buttigieg defended his position.
"Fox is moving more and more to the losing (wrong) side in covering the Dems".
Buttigieg's comments about Carlson and Ingraham come after the Democratic National Committee Chair Tom Perez announced in March that the party will deny all requests from Fox News to host the primary debates because "we can not rely on Fox to host a fair and neutral debate".
The news outlet hosted a town hall with 2020 candidate Pete Buttigieg on Sunday night.
He described the president's Twitter as "mesmerizing" and said it was "hard for anyone to look away".
"I strongly condemn the voices on Fox and in the media that uncritically amplify hate and the divisive sort of politics that gave rise to this presidency", Buttigieg said in an email to supporters on Saturday.
"The tweets are. I don't care, " he said, to audience cheers.
Similarly, when it came time to discuss the recently passed laws restricting a woman's right to choose, Buttigieg explained that often the right-wing sets up questions about later term abortions to try and tear people apart on the issue. "And I trust women to draw the line". "But that decision's not going to be made any better medically or morally, because the government is dictating how that decision should be made".
Specifically, he called out Tucker Carlson, for saying immigrants made the United States "dirtier, " as well as Laura Ingraham, who once compared detention centers for migrant children to summer camps.
Trump added: "Chris Wallace said, 'I actually think, whether you like his opinions or not, that Mayor Pete has a lot of substance.fascinating biography.' Gee, he never speaks well of me".
Buttigieg announced that he would be running for president in January, and officially began his campaign in March.
He has consistently polled at third place among the field of Democratic presidential candidates.
Fellow presidential hopeful Massachusetts Senator Warren has also been rising in the polls in recent weeks.
Ahead of the forum, Buttigieg, 37, had a two-day swing through Iowa, which will hold the first 2020 nominating contest in February.