Ex-Manchester City boss Mancini allowed Tevez to return to the fold despite the Argentine's behaviour in a 2011 Champions League clash in Germany, when he refused to come off the bench against Bayern Munich.
In his new book, My Autobiography, Ferguson has claimed that the Italian "let himself down".
"Taking him back showed desperation. In terms of his prestige as a manager, he let himself down," wrote Ferguson.
Mancini departed City at the end of last season.