Moyle, who is in his 70s, was recovering in Dunedin Hospital after collapsing during the police debrief after the group were rescued, Fairfax reported.
Police contacted Mr Moyle about midnight on Sunday to help the rescue.
"We spent all night servicing them, getting them going and they were ready about 5.30am. We kept ringing the police and getting no reply. When we did get in contact they had changed shift and had to have a briefing. We could have been away by 6am and back by 10am, but we had no communication with them.
"Not one cop came to see us. All they could do was sit in the rugby club eating Jimmy's Pies. No one knew what was going on. It was hopeless. We were putting our own lives at risk by waiting on them. You can't be up there in the dark," Mr Tickle told Fairfax.
Mr Tickle contacted the local policemen at 10am "saying we will go with or without them".
He said, soon after, four search and rescue guys turned up.
"If you ever get stuck in the mountains - don't ring the police," he told Fairfax.
He said him and Mr Moyle drove two snowcats with rescuers on board.
It was a seven-hour round trip to bring the group off the mountain.
A police said in a statement, it was a "challenging operation in difficult conditions".
"...priority for Police was to achieve a successful rescue whilst also ensuring the safety of all involved."
A formal debrief would be held about the operation and would cover the decisions and resources used.
However police disputed "reported claims made through the media by individuals who are not in possession of the full facts about decisions which were made".
"There are always lessons to be learnt from such operations, and these will be established in the debrief to come."
