The Blues currently sit bottom of Group D with one point from three games and face Ajax at the Etihad Stadium on Tuesday in need of a victory.
"I don't think that we are ready to win the Champions League," said Mancini. "If we say this, we are not honest.
"We are a good team. We are not ready like the other teams."
Cit were knocked out in the group stages of last season's competition.