The helicopter crashed about 20m from the helipad pilot Paul Dudley - a long-time friend of the Nicholson family - took off from.
Mr Dudley told his lawyer Robert Hantman he knew there was a problem "immediately".
"He mentioned they had taken off and then he had some mechanical problems. He decided to land. Before he could land, the helicopter went out of control," Mr Hantman told US media.
After the helicopter hit the water, Mr Dudley freed himself and pulled Ms Tamaki and Mrs Nicholson from the wreckage.
"He got them out, released their seat belts, helped them get to the surface. And the third person he wasn't able to get to in time," said Mr Hantman.
Mr Dudley said: "I couldn't get her ... Ten seconds more and I could have had her ... I yelled, I needed help."
Police Lieutenant Larry Serras: "There were two women floating unconscious near the wreckage who could do nothing at all to help themselves. One woman had a severe head wound, and they were face-down.
"I was trying to concentrate on the women. The detectives held the women face-up out of the water. It was tricky. It was tough. We were losing control."
Rescuers on a nearby pier threw a rope to their colleagues in the water and they pulled the survivors to shore. They began chest compressions on the women while they were still in the water.
"We did what we could," said Detective James Coll.
Meanwhile, the helicopter was still sinking with Ms Nicholson trapped inside.
Mr Serras said: "[Mr Dudley] was yelling to us that there was an additional person trapped in the helicopter. By the time we arrived, the helicopter was under. I stood on it for a brief second before it slipped away from me on my feet ... The helicopter had submerged and there was no way we could get to it."
When divers later reached the wreckage at the bottom of the river, they found Ms Nicholson.
"She was unbuckled," said New York Police Department diver Jason Gregory. "She had been trying desperately to get out."
Ms Tamaki, an IT specialist who also lives in Sydney, had organised the trip to New York and the helicopter ride for Ms Nicholson's 40th birthday.
It is understood Ms Nicholson had not seen her family in years and made plans to meet them at the top of the Empire State Building as soon as she and Ms Tamaki arrived in the city. She was said to be afraid of flying, but excited about the trip.
Mr Nicholson was not seriously injured and his wife regained consciousness on Wednesday and was in a stable condition.
Ms Tamaki's mother and sister were on their way to New York yesterday to be at her side. Doctors were concerned that she may have sustained serious brain or lung damage. Her sister Suzanne hoped to know more when her family reached New York, but said Ms Tamaki was getting the best possible care.
