The Reds central defender hit out at US owners Tom Hicks and George Gillett for failing to back Benitez in the transfer market, while he was also critical of his manager's willingness to put his pride before the good of the club.
In his autobiography, Carragher says he was disappointed with the dirty linen being washed in public at Anfield, while admitting he thought there was some truth in stories linking Jurgen Klinsmann with the managerial position.
"I believe he suspected a plan was already in place to sack him and the owners were holding back funds for his replacement," Carragher said in extracts carried in the Daily Mail.
"He was effectively daring the owners to arrange his funeral, especially when Hicks ended the boardroom silence by telling him to shut up on the front page of the local paper.
"It was more than rumour by this stage, and Rafa must have known how close he was to the sack. To my mind, everyone was trying to be too clever, playing politics with little regard for how much damage it was doing.
"Never mind about not washing your dirty linen in public, Anfield was beginning to resemble a launderette."