You lost not because of the refereeing, but because Mancini settled for a draw when it was yours to win. Bringing off Aguero and Silva and replacing them with defensive players Toure and De Jong with quarter of an hour to go let Chelsea in.
Mancini is a defensive manager by nature and City spent all last season repeating this same mistake, bringing on defenders to get a draw when you should have been going for the win. City have been getting 4 or 5 goal leads so Mancini hadn't done it so far this season, but the first time City find themselves on equal terms, Mancini reverts to his old ways.