Mancini was sacked last week after three-and-half years, leaving coach Brian Kidd to lead the City squad on their week-long post-season trip to New York and Saint Louis.
Clichy said: "We have to take responsibility for this season and yes, probably, it's because of the manager that we haven't won anything. Because he's the man in charge but also because of us as players.
"He's the manager and you have to take responsibility. The manager is there to make the choices.
"Of course, when results are good it's all down to the manager. When the results are not so good, it's also down to him.
"We have to be aware that he was probably at fault for this, but as players on the pitch we also have to take responsibility and also know that we didn't perform.
"You have to give 100 per cent and sometimes this year we didn't give anything."