The Italian has come under fire this season following his side's exit from the Champions League and failure to compete with rivals Manchester United in the Premier League.
Shearer wrote in his column in The Sun: "Mancini will know what it needs to make City bounce back. The mistakes of last summer will not be made again.
"They will come back stronger. City are building something still and to change the manager who has done so much to start it all would be wrong.
"Unless they want to be regarded in the same vein as Chelsea, whose knees jerk at the slightest slip-up, they need to keep faith with Mancini."
City all but conceded the title to United following their defeat on Sunday to Tottenham Hotspur.