"When we started seeing the fuel being unloaded we realised something was wrong."
FlightRadar24 showed the aircraft made at least a dozen full circles before returning back to Doha just over an hour after take-off at 3am Doha time.
Riley said it was only once the plane touched down that they realised the extent of the damage.
"We got down there and they surrounded us with water cannons and there was flashing lights all over the place.
"We were taken straight off the plane, but we didn't know the real reason until we saw it for ourselves," he said.
"On the port side engine you could see the hole in the side of it. It was about 400mm by 400mm."
Despite the concerning damage, Riley applauded the pilot and staff for their reaction.
"All in all when we did land everybody clapped and were pretty relieved to get down.
"I thought the captain was excellent, and kept us informed right the way through. We didn't know exactly what it was but we didn't feel any problems."
The Qatar Airways flight, QR920, had been due to arrive in Auckland at 4.45am this morning.
Riley said the incident caused a five hour delay to their journey, which totalled 34 hours.
"A lot of people missed their connecting flights this morning, but for us it just meant my daughter had a lie in," he laughed.
"We are exhausted, but glad to be back."
The airline confirmed the Auckland flight returned to Doha following an engine issue.
"Qatar Airways can confirm that flight QR920 flying from Doha to Auckland Airport declared an emergency due to a technical fault following take-off and returned to Hamad International Airport.
"The crew took all necessary precautions and the aircraft proceeded to land safely and without incident.
"We apologise for the inconvenience caused to our passengers," it said.
Aircraft Facts:
Qatar's Boeing 777-200LR (longer range) aircraft are powered by two GE90 engines, the most powerful in commercial aviation now.
The engines generate close to 110,000lb of thrust or about 100,000 horsepower each.
The plane would have been loaded with around 170,000 litres of fuel for the 17-hour plus flight between Doha and Auckland. It is the second longest non-stop flight in the world behind Singapore to New York.
The aircraft on Sunday had climbed to an altitude of about 2000m before the engine failure. It returned to Doha 1 hour and 19 minutes later.