City already appear out of the Champions League this season.
Mancini said: "In two years we've won three trophies. Do you think we will let our heads go down after one defeat?
"If we are like this after one defeat then we are really weak but I don't think we are. We're strong enough for this.
"I don't think we've finished our job because we won the title last year. We have to work more as it's not easy to win the Premier League.
"The challenge is to stay on the top for a long time. For this you need to work more than last year.
"We know we will have defeats but if we want to stay there, we have to get over these situations."