"Don't get me wrong, I'm embarrassed by that letter, more so I'm embarrassed that I caused distress to a family," he said.
"But even worse, we're talking about an 11-year-old girl who I have re-victimised, and I'm really embarrassed and sorry about that," he said.
Mr Gibson said his error was not a reflection of an attitude within the police service.
He had written to the girl's family to apologise for the statement but they say that was not good enough.
"It makes me question the police system, it makes me question the court system, and it makes me question what we call ... justice," a family member told 3 News.
The family member, who was not identified, said the girl was now a teenager struggling with self-harm.
The police had let the family down "so, so much", said the family member.
Abraham, from Palmerston North, was convicted in 2010 of sexual violation by rape and sentenced to 10 years in prison.
He had begun sexually grooming the girl in 2008 when she was 10, progressing to rape after a year.
In her victim impact statement read to the court at Abraham's sentencing in September 2010, the girl said her life had been "perfect" until she turned 10 and the abuse began.
"My life was turned upside down," she said. "I didn't feel safe at home and I used to hide from him when he came to our house."