Mr Morrison told financial analysts SkyCity was unwilling to contribute more than $10 million to the funding gap without compensation for his shareholders, and floated the possibility of financial support from central or local government.
Earlier this month Prime Minister John Key told reporters he could not rule out taxpayer money being used to meet some of the cost overrun, but negotiations were ongoing and nothing had been taken off the table.
Mr Key had said a convention centre built for the initial figure could be an "eyesore", but "the Government's preferred position is that SkyCity completes the convention centre for $402 million".
Mr Joyce today said there would be no change to the concessions offered to SkyCity. "We ruled that out right at the very beginning."
The downsized convention centre may end up being around 10 per cent smaller than previously planned "but no more than that", he said.
"By allowing it potentially to be a little smaller, we alleviate some of the increased cost that they've been concerned about."
Following Mr Key's "eyesore" comments, Mr Joyce said SkyCity was strongly motivated to build an attractive convention centre.
"Otherwise it would completely cut across the reasons why people have been involved in this project. I'm confident that they'll come up with a good design."
Negotiations with SkyCity had been "robust", Mr Joyce said.
"We've also had a lot of private discussions where we've made [it] very clear that we don't see a role for the Crown to put any significant sums of money in.
"I think once they realised that we were pretty definite about that, we were able to come to a conclusion."
SkyCity chief executive Nigel Morrison said the company respected and accepted the Crown's decision.
"This decision gives SkyCity the clarity needed to move forward with the development of this exciting project.
"We remain committed to delivering a landmark convention centre for Auckland and New Zealand."
Leader of the Opposition Andrew Little said overwhelming opposition to public funding for a convention centre meant the Government had no choice but to back away from its plans.
Green Party gambling spokeswoman Denise Roche said the backdown was a "victory for everyone" as no taxpayer money would go towards SkyCity casino, "just as no laws should have been changed to allow the casino to build more pokies that will inevitably cause more gambling harm".