The column comes nearly three weeks after his father's jailhouse suicide.
The 53-year-old held three women in his home for nearly a decade. Ariel Castro kidnapped the women between 2002 and 2004 when they were 14, 16 and 20 years old.
He housed them in brutal conditions, restricting access to food and toilet facilities, chaining them and beating and raping them repeatedly. He fathered a girl with one of the victims.
One of the women escaped May 6 and alerted authorities.
He was a month into his life sentence when he committed suicide by hanging himself with a sheet attached to a window hinge in his prison cell.
"Instantly, my father became one of the most hated men alive, Anthony Castro writes in the Plain Dealer column which was published Sunday. "In no time, reporters from around the world demanded to know who this man was and what kind of background he came from. Just like that, my father went from captured to convicted to imprisoned to dead."
In the column, Anthony Castro writes he was "horrified and disgusted" by his father's acts and remains angry that his father killed himself in prison.
"He deserved to pay for his actions, every day of those 1,000 years he could possible serve," Anthony Castro writes. "My anger with him kept me from visiting him in prison, even when he was moved to a facility just 20 minutes away from my doorstep."
Anthony Castro hopes his father's life and death can lead to changes in handling sexual predators, domestic violence, mental illness and prison safety.
"If we can prevent a repeat here or anywhere, then justice truly will have been served amid all the broken pieces my father left behind," he writes.
The Associated Press contributed to this report.