He said he began to veer off the runway as he was attempting to reach the brakes and could see a wall rapidly approaching.
"I thought 'I ain't going to do it,' but we managed to stop in the end," he said.
Emergency services were waiting when the plane touched down, after a few bumps.
Rob Murray, one of the flight instructors, said he was glad to have helped and that Wildey did a "remarkable job," given he had never flown a plane before.
"It's a fantastic feeling, knowing I have achieved something and probably saved somebody's life," Murray said.
He said the atmosphere in the control tower was tense and there were handshakes but no cheers when the plane touched down.
The emergency landing occurred not far from Sandtoft Airfield, where the plane had planned to return after a short flight.
At a news conference at Humberside Airport, commercial director Paul Litten expressed his condolences to the family of the man who died. Police said an inquest will be carried out to establish what caused the pilot's death.