I don't believe he has let the manager down. I think Mancini left him on the pitch deliberately hoping he would get sent off. Mancini has lost patience with the boy. What better outcome for Mancini than to watch his prodigy get sent off yet again, so that Balotelli becomes the focus of everyone's anger, and the scapegoat to boot.
How many people are talking about Mancini's management or tactics at the moment? Very few. How many people are blaming Balotelli for losing us the league? Very many. It suits Mancini that someone else is to blame for our failures.
Balotelli therefore has to go. It's the only way Mancini can save face, and possibly his job. Plus, what top professional would want to come to a club where there is this character liable to get sent off and cost his team games, when they want to win trophies. You can see how players have lost patience with him. I think they have had enough of the side-show, and they want to knuckle down and win games and trophies without the added distractions. I'm fed up of it all too, and I suspect the majority of City fans are.