City have again failed to reach the knockout round of the Champions League this season.
"We didn't do well and for this reason, they are disappointed," he said. "But they said they understood it takes time to succeed in the Champions League.
"When you are new to it, you have to work at it and that is what we will do."
On talk of City agreeing terms with former Barcelona coach Pep Guardiola, Mancini added: "(The chairman Khaldoon Al Mubarak) is happy with the way we are going in the Premier League and there is still the FA Cup to come."