The Italian has come in for criticism from some quarters following Wednesday night's 3-1 defeat away to Ajax in the Champions League.
Mancini's tactics on the night were called into question but Holloway believes that it would be a mistake for City to remove the former Inter coach from his current post.
"I know we live in a world of sensationalism, but sometimes people who are paid to offer opinions on such matters really do need to get a grip of themselves," said Holloway in his column in The Mirror.
"Within minutes of City's 3-1 defeat I heard one TV pundit suggest Mancini had lost the dressing room and that he is on the slippery slope that leads to the job centre.
"Mancini is the man who five months ago won the greatest championship race of all time for Manchester City. It was City's first title for 44 years."
City have just one point from their three Champions League games this season after they followed up a 3-2 defeat at Real Madrid with a 1-1 draw at home to Borussia Dortmund.