New Zealand's dramatic Rugby World Cup quarter-final win over Ireland was founded on four years of "adversity and hurt", former All Blacks said Sunday.

The three-time champions were hailed for their defence during their thrilling quarter-final win in Paris after resisting waves of Irish attacks in the nail-biting closing stages.

Many pundits had forecast victory for the top-ranked Irish, who triumphed in a series on New Zealand last soil last year, a historical first which sat among a series of lows for the All Blacks since Ian Foster became head coach in 2019.

Foster and captain Sam Cane had absorbed plenty of criticism after poor results last year before their side arrived at the World Cup ranked fourth in the world.

However, former All Blacks greats Mils Muliaina and John Kirwan said Sunday that Cane and Foster deserved praise for the fighting nature of the victory.

"All the adversity and hurt. You've got to go through some of that to come out and perform the way they did today," Muliaina told local broadcaster Sky.

"The desperation that they showed at the end there, they stayed connected and they believed.

"For Sam Cane, for all that he's been through, and Ian Foster, they've been through hard times and they've turned that around into something special."

After winning the World Cup in both 2011 and 2015, the All Blacks have been smarting since losing to England in the semi-finals of the 2019 tournament in Japan.

New Zealand captain Cane was majestic in the win over Ireland.

Kirwan described the injury-plagued flanker's display as "epic", noting how the captain led from the front when New Zealand were twice reduced to 14 men by yellow cards.

"We were way more physical than they were tonight and it started with Sam Cane," Kirwan told Sky.

"Ireland were outstanding right to the death but even with the yellow cards, our guys stayed calm, they stayed disciplined.

"This team's come together, they're peaking at the right time and they showed incredible courage."

The New Zealand Herald described the quarter-final as "one of the great World Cup Tests".

Another of their headlines said the maligned side had "answered their moment of truth with an astonishing win".

While Ireland's performance was widely praised, Kirwan offered a stark assessment of Irish failure to advance past the quarter-finals for the eighth time in eight attempts.

"If you can't get the monkey off your back, it turns into a gorilla," he said.

"It's now a gorilla for them. You carry the weight of expectation on your shoulders and it just gets really tough."