West Ham travel to the deposed champions on Saturday.
Allardyce said: "If City win the FA Cup and finish second, then they have had a successful season.
"Unfortunately for them, they have been chasing the master, Sir Alex Ferguson. He has been the master for so long and it's very difficult to sustain success against him.
"He might lose out one year but the following season he's back with flying colours. When you win the title for the first time, it's very difficult to repeat it the following season."