The England international, who has put in a number of questionable performances so far this season, was dropped for his side's 7-0 win over Norwich City on Saturday, with Costel Pantilimon replacing him in goal.
"If the quality is a bit off, you must work harder to recover your position and your best quality," Fernandinho told reporters. "If he at the moment is not [at his best], he must work harder.
"But they are very good keepers, he and Pantilimon. I think his career will be better for it.
"The manager must choose the best team, and the best keeper for the team."
City host CSKA Moscow in the Champions League on Tuesday.