The family "really appreciate everyone's support", he said.
The couple, from Waitara, northeast of New Plymouth, were reported missing after the single engine plane failed to reach Stratford Aerodrome, after taking off from Whitianga on Sunday afternoon.
A large-scale search and rescue operation was launched, including a fixed-wing aircraft and a Royal New Zealand Air Force helicopter, which scoured an area around the couple's last known location.
However, poor weather and poor visibility hampered the search, and it resumed the next morning. The pair were found by the Taranaki Rescue Helicopter around 11am, after spending a cold night in dense bush.
On Monday afternoon, Adam Warner told media his father had managed to put the small aircraft down in thick bush after hitting bad weather on Sunday evening.
He said he was relieved but somehow unsurprised his parents survived largely intact. They were "a bit shook up" by the incident, however.