"Without the CRL, Auckland will hit gridlock and the city will grind to a halt," he said.
He said $250m of the additional costs was being used to "future-proof" the rail project. This included building longer platforms at stations so trains with more carriages could pull up.
A further $300m in added costs was being held "as a contingency against any potential cost escalations".
"Without additional funding, the CRL would not have been fit for purpose," Goff said.
"We would have had another Harbour Bridge on our hands which was built at half of the size it needed to be and had to have major additions made to it within eight years."
"We've got one shot at getting the CRL right."
Two of the 21 council members voted against stumping up the half a billion dollars in extra cash.
"Auckland ratepayers should not be paying another cent towards this project, and central Government needs to step up to the plate and fund 100 per cent of the project, as they do for every other city rail project across the country," councillor Greg Sayers said.
"Councillors were effectively strong-armed into approving the $1 billion overrun without knowing who actually owns the CRL assets, who is paying for the ongoing running cost or how much the ongoing running costs will be."
"I refuse to make decisions without having all of the critical financial information."
The council decision comes after City Rail chief executive Sean Sweeney earlier this month said the $1b budget blowout had been due to a range of factors, including higher construction costs and a decision to build bigger platforms to allow longer trains to pull up.
But Infrastructure NZ chief executive Stephen Selwood said part of the blowout had also been due to political pressure to underplay the estimated project costs so voters weren't scared off by its price tag
It was an unfortunate reality of mega-projects around the world that their costs were often undersold, he said.
This was partly because politicians wanted the lowest number possible to present to taxpayers and partly because short election cycles forced them to push projects through before detailed cost analysis could be done.
"Politicians are keen to make progress fast, they are in a very short-term election cycle - only three years in New Zealand ... and numbers are quoted that are usually not that well-researched and robustly analysed," he said.
"Then when you launch a full scoping of a project you almost inevitably find it is much more complex and costs go up."
Goff said council would raise the extra $500m through a number of measures.
These included savings made as a result of low interest rates that had led to smaller repayments on council loans, a reduction in "cash holdings", and selling or leasing council-owned carpark buildings.
