58-year-old Chavez Sr, who fought his own exhibition against Hector Camacho Jr, said: "I prefer that they retire if they are not going to prepare correctly.
"They do not prepare in the best way possible to fight."
Anderson Silva earned a split-decision victory at the Estadio Jalisco in Mexico.
Silva made his pro boxing debut way back in 1998 then tasted victory at the second time of asking seven years later before focusing on UFC.
And the 34-11-1 former MMA middleweight champ did enough in his third boxing fight to earn the win.
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Boxing as a southpaw, the Spider pulled out vintage moves to dodge and weave the swings from Chavez, taunting him all the way with some trademark showboating.
He landed a huge uppercut in the fourth and after that, Chavez struggled to make his mark for the remainder of the eight rounds.
The sluggish Mexican came in overweight for the limit, forcing him into a £72,000 fine paid to Silva.
And he was bloodied and bruised by the time the judges called it 77-75, 77-75, 75-77 to his opponent in his 60th pro career.
Canelo Alvarez was on hand ringside to congratulate Brazilian Silva on his victory.
Mexican legend Julio Cesar Chavez shows off incredible punching strength aged 58 in training video