Mr Acosta stood up and began to ask a question relating to the statements Mr Trump made at the end of the midterms campaign.
Appearing on CNN on Wednesday evening, Acosta told host Anderson Cooper: " I was just trying to ask a question of the president.
"CNN should be ashamed of themselves, having you work for them", he said.
Trump added that the way Acosta had treated Press Secretary Sarah Sanders was "awful". He was heading back to the White House for a live shot on "Anderson Cooper 360".
"(Sanders) provided fraudulent accusations and cited an incident that never happened.
Acosta called the claim a "lie".
Acosta has always been a bitter adversary of the White House. "And the way you treat other people is frightful".
Stirewalt said that either way, the episode hurts the political discourse as the Acosta-Trump feud overshadowed "a bunch of good questions" from reporters like Fox News' John Roberts and CBS News' Major Garrett.
"This unprecedented decision is a threat to our democracy and the country deserves better", the statement concluded.
"Contrary to CNN's assertions, there is no greater demonstration of the president's support for a free press than the event he held today". As the Joker put it in Christopher Nolan's The Dark Knight: "I don't wanna kill you".
The president clashed with Acosta after a series of questions about the migrant caravan, but the conversation became personal in a hurry. "When you report fake news, which CNN does a lot, you're the enemy of the people".
He also posted a tweet saying he was stopped by the Secret Service from entering White House grounds.
Some Democrats in the House of Representatives, where the party now has a majority, have threatened to use the subpoena power they will gain in January to investigate Mr Trump and his administration's actions.