Mr Key said organisers either "hadn't thought through every single contingency or hadn't acted on every potentially known contingency".
"I think you can see that there was an operational failure in part of the system."
Auckland Mayor Len Brown and transport bosses are scrambling to restore public confidence in the city's train service before Saturday's cup clash between Australia and Ireland at Eden Park.
More than 54,000 tickets have been sold for the game.
Auckland Council transport chairman Mike Lee said Veolia had to take a large share of the blame.
"Everything we have worked for in the last five years ... we were let down - it was a disgrace."
Tomorrow, Mayor Brown is to receive a review of the rail problems from Auckland Transport chairman Mark Ford and chief executive David Warburton.
Mr Lee has called a special meeting today to discuss Friday's events.
A council source told the Herald that "Veolia hasn't stepped up to the mark as well as it could have done", saying the train operator had previous performance issues, including at U2's concert last November when a passenger pushed a stop button and stranded several trains near Ellerslie station.
Mr Lee said it was time Veolia started earning its management fee of about $35 million within total annual rail funding of $85 million.
But Veolia chief Graham Siberry defended the firm's efforts.
"Ultimately we got swamped with the numbers and had safety incidents, and that made life very difficult.
"We don't come to work to try to muck people about."
Last Thursday, Mr Ford told councillors that just about every eventuality for transport had been planned.
"But whatever you plan for, there is always going to be an act of God. I hope the good Lord is on our side."
Auckland Transport has set up a hotline and website as the first step to providing compensation for people who missed the action at Eden Park.
Veolia said problems began when 60,000 people - four times more than its normal patronage - caught the trains that day.
These problems were compounded by safety scares, including people riding on the outside of a locomotive, assaults and fights.
As well as the five incidents of emergency stop buttons being pressed, a fire extinguisher was fired into a closed carriage. "Safely managing these incidents was our principal focus while maintaining the train services," said Mr Siberry.
He said the unjustified use of emergency stop buttons was a problem the company would try to tackle over the next week with Auckland Transport.
As well as the transport problems, another issue is that instead of providing additional fanzones at Henderson, Manukau and Albany on Friday night, cup organisers put all their resources into "the biggest party Auckland has ever seen" on the waterfront, knowing Party Central on Queens Wharf could accommodate only 12,000 people.
But about 200,000 people poured into downtown Auckland.
Problems were compounded when one side of a double-sided television screen on Quay St failed and people poured over to the Ferry Building side of the screen, which was still working. The crush led to the cancellation of ferry services.
A second television screen failed in the Viaduct Harbour. The six screens used along Quay St on Friday have been removed. Several screens on Queens Wharf will be available for the rest of the tournament.
Auckland Chamber of Commerce chief executive Michael Barnett said history should have told Auckland Transport that rail alone was never going to cope with a sold-out Eden Park.
"A bus-based back-up transport system is essential for the next big game at Eden Park," Mr Barnett said.
He said organisers knew weeks ago that 150,000 people would be at the waterfront for the cup opening, and more venues should have been set up.
Rugby World Cup Auckland Co-ordination Group chairwoman Rachael Dacy defended the decision to concentrate the opening ceremony celebrations on the waterfront.
The fanzone, from the Viaduct Harbour along Quay St to Queens Wharf, was designed for 50,000 to 60,000 people, she said.
Organisers expected twice that number and opened up Quay St to the Vector Arena and the Wynyard Quarter.
"Once that site filled, we controlled access into the area and sent out messaging immediately, 'Don't come down to the waterfront, we are full'," Ms Dacy said.
She said $2.7 million was spent on the waterfront celebrations, and there was no money for the significant cost of operating fanzones at Henderson, Albany and Manukau, which will not be opened until the quarterfinals.
