The public have been warned not to approach the pair, who are believed to have hitch-hiked out of the city on Monday night.
Dave Macpherson, father of Mr Stevens, told TV3 he had "pleaded" the staff at Henry Rongomau Bennett Centre against letting his son out for fears he would harm himself.
"We complained well in advance of him disappearing about the management processes and security processes that lead to him getting out."
Mr Macpherson said following his son's death the facility began an internal inquiry, but he asked for an independent review.
Waikato District Heath Board chief executive Nigel Murray told TV3 that an independent review would be carried out following the escape of the two patients on Monday.
Mr Macpherson said his family was "very hurt" that it took a second incident for the review to come.
"It means our son's death doesn't count for anything in that sense.
"Where was the answer to us, the response to us when we requested a proper review and an independent review?"
"We feel very hurt that it didn't happen because of what happened to our son."
Mr Macpherson said Dr Murray had never spoken to his family after his son's death.
Dr Murray told TV3 that the two scenarios were "quite different circumstances".
He said he had expressed his "deepest condolences" publicly to the family of Mr Stevens, but would not be speaking to the family until after the review.
Senior Sergeant Andrew O'Reilly of the Waikato District Command Centre said the escaped patients are known to have contacts throughout the Waikato and Bay of Plenty.
"Advice from medical staff suggest neither man poses specific risk to the public, however both have a history of violence and police advise the public not to approach them but to ring 111 if they are seen."
Where to get help:
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youth services: (06) 3555 906
• Youthline: 0800 376 633
• Kidsline: 0800 543 754 (4pm to 6pm weekdays)
• Whatsup: 0800 942 8787 (1pm to 11pm)
• The Word
• Depression helpline: 0800 111 757 (available 24/7)
• Rainbow Youth: (09) 376 4155
• CASPER Suicide Prevention
If it is an emergency and you feel like you or someone else is at risk, call 111.