The five-eighth was absent when the All Blacks assembled to leave their airport hotel for the flight to Santiago on Sunday morning.
Cruden has been stood down for the rest of the Rugby Championship and may also face internal disciplinary charges and a fine.
Yesterday, while offering no excuses, he issued a statement saying it was unacceptable to miss the team assembly.
"I am deeply embarrassed by this lack of judgment and have never been more disappointed in myself. I have not only let myself down but, most importantly, I have let my team down.
"I carry the burden of shame and disappointment and I am deeply apologetic to my team, to my family and also the New Zealand public.
"I have been working really hard over the past few years at gaining the respect on the field as well as off the field and am devastated I have dropped my own high personal standards, as well as the standards set by New Zealand Rugby.
"I accept full responsibility for my actions and the penalty of missing the next two games, and will work with New Zealand Rugby to undertake any other disciplinary action to work through this situation."
Cruden and other All Blacks went to the Zookeeper's Son at Royal Oak on Saturday after their earlier flight to South America was delayed because of mechanical issues.
Bar owner Dave Catchpole said the group arrived about 8pm. "It was really just a relaxed dining night out. They sat in front of the fire for about four hours, ordered fish and chips, burgers and the big Canterbury roast.
"They had no more than two or three beers each, so it was a very ordinary night. They played a bit of pool, didn't get hassled much and posed for a few photos ... "
Mr Catchpole was not at the bar, but said he'd spoken to his managers. They said none of the All Blacks seemed intoxicated. Their tab came to "close to $600, or about $80 a head", before they left in two or three groups about the same time.
Cruden, 25, eventually made his way to the Little Easy bar in Ponsonby rather than to the Airport Novotel, where the team were staying.
It is understood he also went to the Long Room on Ponsonby Rd.
Yesterday, Cruden did not answer questions when the Herald approached him at his Hamilton home. His agent, Bruce Sharrock, instead said he was "having a debrief".
Cruden's behaviour could cost him thousands, with the All Blacks' weekly assembly fee of $7500 in jeopardy and fines also on the radar.
The head of the NZ Rugby Players' Association, Rob Nichol, said the disciplinary process would determine what happened to Cruden next. Options ranged from a warning to termination of contract, he said.
According to the collective agreement, Cruden could be fined up to $4000 if found guilty of serious misconduct, or $500 for misconduct.
"The money is probably the furthest thing from his mind. It's actually about thinking through the process and recognising why it happened and how it happened."
Other players had made amends through speaking at schools, community service and apologising to the respective parties, Mr Nichol said.
All Blacks coach Steve Hansen said the team hadn't been subject to a curfew on Saturday night but Cruden was out drinking and "didn't get there on time" to catch the flight.
"He understands there has to be a consequence for his actions. Once we get this out of the way, he'll be coming back into the group when we go to Brisbane [for the third Bledisloe Cup test]," he said from Argentina.
"It's certainly out of character and he's disappointed, as are we ...
"I guess we all make mistakes and, like our children, we love our children, but sometimes we don't like their behaviour."
