Sage, 36, who starred alongside his father in "Rocky V", was found dead in his home on Friday of an apparent overdose, reported E! online.
Sylvester said Sage was the centre of his and ex-wife Sasha Czack's lives.
"Sage was our first child and the centre of our universe and I am humbly begging for all to have my son's memory and soul left in peace," he said.
The 66-year-old action star has also requested to show respect for his late son.
"This is in reference to the speculation and questionable reporting surrounding the death of my son Sage. Because when a parent loses a child there is no greater pain.
"Therefore I am imploring people to respect my wonderfully talented son's memory and feel compassion for his loving mother Sasha, because this agonizing loss will be felt for the rest of our lives," he said.
