"[It was] business as usual, and then it literally collapsed beneath our feet," he said.
He told Radio Sport critically hurt people were lying everywhere after the incident.
"None of the boys are hurt or injured though - so that's good."
"But everyone's a bit shaken up."
Small said he and a few teammates had been enjoying themselves moments before the incident.
"We were just dancing and then the next minute we dropped 5m to 6m and everyone started rushing out of the club after that.
"We, I guess, fell on top of the heads of other people that were beneath us."
A few of the men's team tried to get some of the injured out from under the rubble.
"We did what we could, but we couldn't really do too much. Some of them were pretty dire cases."
"We were more so just concerned about everyone else, we were trying to do a number count and make sure all the boys were there.
"And everyone was fine - so pretty relieving stuff but at the same time pretty chilling."
He said there were probably between 10 to 15 New Zealand men's and women's water polo players in the club.
The players did a headcount outside the building and then jumped into taxis and headed to their hotel amid a chaotic scene as ambulance and police cars descended on the scene.
Small said the men's team would spend today in the city of Gwangju before catching a bus to Seoul tomorrow and then a flight to New Zealand.
He didn't know how many people were injured in the incident but saw multiple people lying on the ground who looked like they were dead as he made his way out.
Chris Wilson, the chief executive of NZ Water Polo, confirmed to Radio Sport all the New Zealand players were safe.
"At this stage, there are no serious injuries, a couple of our women's players had some minor injuries, but all the New Zealand players are safe and well and accounted for," he said.
Wilson said reports the men's players had helped the injured made sense.
"Like any situation with human nature where people are under a bit of pressure people do rise to the occasion, and I'm sure that part of the New Zealand team they would rise to that occasion themselves," he said.
"That's the sort of thing we do when we get into these type of situations."
A Korean news outlet reported the incident took place at 2.39am in the southwestern city of Gwangju and the injured had been taken to hospital.
The seven-storey building had hundreds of guests and employees inside it. The structure that collapsed was about 4m high.
Water Polo Australia confirmed members of its women's bronze medal-winning team were also present at the club, according to news outlet ABC.
It quoted a Water Polo Australia spokeswoman saying the team was "deeply shocked" after witnessing the collapse.
However, all the Australian players escaped uninjured.
Both the New Zealand men's and women's team had finished competing at the world championships and were scheduled to fly home today.
"It's been a busy two weeks for the New Zealand men's and women's teams at this championships," Wilson said.
"We had an outstanding result for the New Zealand women - finishing 12th, one of the highest placings in a 16 team tournament."
"The New Zealand men's not as strong in 16th, but a very high-level competition."
