Mr Vereker-Bindon spoke to the Herald from ship MV Cap Capricorn, which rescued the group from a sinking lifeboat on Wednesday.
His 15-metre yacht Sunny Deck is now burnt-out at the bottom of the Pacific Ocean - and Mr Vereker-Bindon said a series of lucky escapes kept him from "undoubtedly" joining it.
"It was just a miracle. I counted we had about five ways to die. It was pretty close.
"We've come off with no money no passports, just the clothes we were wearing. And we're alive. That's a blessing. Everything else is replaceable."
The two Kiwis were woken by the captain's yells about 1.30am as the yacht pitched in 5-metre swells.
The engine had caught fire and heavy smoke was billowing through the ship making it difficult to see, Mr Vereker-Bindon said.
Within minutes of the trio getting onto the deck "really furious" flames erupted out of the area where they were asleep.
They jumped into the lifeboat in just boxer shorts and t-shirts, cutting themselves loose of the burning ship for fear of explosion but puncturing the lifeboat in the process.
The electronic rescue signal machine had been fire damaged and they were not sure whether it would work.
Metre-high waves were lashing the lifeboat and bringing more water on board as the men furiously tried to bail it out, Mr Vereker-Bindon said.
They heard an explosion as Sunny Deck went down.
"We were in the raft and talking about how long we would last.
"We were wet, cold...every now and then a wave would break on top of us and flatten the canopy onto us and put some more water into the raft and we would try to bail it out again."
It was four hours of bailing water and sending up prayers in English and Mexican before the men had a stroke of luck.
Two lights hundreds of metres in the distance heralded the Hamburg Sud cargo ship heading right for them.
Mr Vereker-Bindon said he had not seen another ship the whole way between Rarotonga and Tonga, so the feeling of relief was overwhelming.
But the hardest part was still to come - paddling for an hour in the rough seas to reach the ship and then getting on board.
Just as Mr Campos, the last of the men to leave the lifeboat, got onto the ladder the whole raft broke free from the rope and disappeared into the swell.
"In the big seas trying to paddle that raft is just too difficult to describe. That's probably one of the toughest hours of my life," he said.
"Of course the ship was rising and falling in the sea and we're rising and falling in the raft as well. If anyone had fallen into the water the captain said there was no way he would have been able to pick us up again."
He said the journey from Mexico to New Zealand was a "bucket list" trip that just went wrong because of "bad luck".
The main thing he was looking forward to doing was seeing his family when Cap Capricorn docks in Auckland on Saturday.
"I'm looking forward to seeing my family. We'll be a bit late, we're in a big sea out here in 50-knot winds...I'm almost pleased we're not on Sunny Deck out here, I guess.
"That's the risk of failing. You're always at risk on the sea and if you think you're not, then you're in trouble."
Mr Vereker-Bindon's son Matthew Vereker-Bindon had been tracking Sunny Deck on its journey and was first to hear of the drama.
He called his brother Andrew to deliver the news at 6am.
"The first thing he said was that they were all safe," said Andrew.
"I knew that everything was going to be ok. It was a pretty big shock though because my dad's pretty cautious when it comes to these sorts of things."
Mr Vereker-Bindon splits his time between Mexico and New Zealand, where he worked as a lawyer.
He and his wife run a student exchange programme in Acupulco, offering school exchanges between students from Mexico and New Zealand.
