Some comments label those pictured as "cowardly scum", "lowlifes", and "feral", while other comments focused on physical appearance.
"He can't hide his ugly mutt," one commenter wrote on the Auckland City District Police page.
"This trash needs a bullet," someone else said on a Counties Manukau Police page.
"A wild sasquatch appears. Quick throw your pokeball," a comment on the Canterbury Police page said.
Another post on the page seeking information on the whereabouts of a 28-year-old woman who had breached her bail drew the advice: "Try Eastgate KFC."
Cocker said it "made sense" for police to use social media as a way of tracking down wanted people.
"Whether any of that feedback is, you know, necessary, is debatable."
He said the comments "can be" harmful, but it was the responsibility of the police to manage the reaction to pictures. Police must weigh up the public interest with the potential harm, he said.
People "absolutely" had the right to complain to Netsafe if they believed the comments fell under the Harmful Digital Communications Act, but Cocker said the act was mainly put in place to protect people from harassment.
Comments had to be "pretty extreme" to qualify.
The test under the act was that comments had to be aimed at an individual, had to breach one of the communications principles, and had to cause harm.
"To be officially an offence you've got to meet all of those."
He said nasty comments on the internet were "part of life in a free society".
All New Zealand Police Facebook pages have a moderation filter running in the background which automatically hides comments containing profanities and inappropriate language, a police spokesperson said.
"However, this doesn't mean it will hide all negative comments.
"The Public Affairs team at Police National Headquarters works with each police district to moderate comments and hide anything racist, sexist or discriminatory. We do look out for negative comments and have on occasion requested that people be respectful in their comments. "
Across the 15 NZ Police Facebook pages, there are more than 730,000 followers, and pages receive hundreds of comments every day.
"It is not always possible to monitor and moderate every post. It's important to note that our followers will also self-moderate and address disrespectful comments themselves.
"We have not received many complaints about Facebook comments. The most recent one was about a Chinese constable in Auckland who did a short video in Mandarin. This unfortunately resulted in some racist comments but we intervened quickly and hid all racist comments and questions from the post."
Anyone who wants to complain about harmful comments about them on the internet can contact Netsafe on 0508 638 723 or queries@netsafe.org.nz, or fill out an online form.