City beat European champions Bayern Munich 3-2 at the Allianz Arena on Tuesday but did not send on leading scorer Sergio Aguero to chase the one further goal they needed to top Group D because Pellegrini thought his team had to score another two.
"It’s a *****-up," said Hamann. "It shouldn’t have happened. The whole City coaching staff haven’t covered themselves in glory here. It’s a poor effort.
"They say the manager is only as good as his backroom staff. He must have had six, seven, eight people around him. For none of them to know and make him aware of the magnitude another goal would have is ridiculous and scandalous in a way.
"Even a player doesn’t go to the manager and say, 'Bring Aguero on'."
"Bayern made £60-£70million by winning the Champions League. Going out at the last 16 could cost millions of pounds."