The All Blacks face the world number one side in Paris for a place in the semi-finals and a win would also end Ireland's 18-match unbeaten run.
Andy Farrell's Ireland raced through Pool B with victories over Scotland, Tonga and Romania and managed to edge World Cup holders South Africa, despite failing to score until after half an hour against the Springboks.
"I think if the Irish are allowed to settle in, they're pretty well drilled and they know how they do things," two-time World Cup winner McCaw told AFP.
"If you disrupt that I'm not sure they've really had to get themselves sorted there.
"That will be the main thing - to make sure they don't get their own way, especially early on," he added.
Thanks to their imperious recent form Farrell's men are favourites for the game in Paris but 148-time All Black McCaw said Ian Foster's squad backed their chances.
"That's what we all think, the underdogs," icon McCaw said.
"That's not what they think. They believe they are good enough to win.
"From the fans' point of view it is a bit different, you go 'I'm not sure if the All Blacks are good enough to win.'
"I know from within they think they can," he added.
'Turn the dial back'
Ireland are on an impressive run against three-time World Cup winners New Zealand, having won five out of their last eight meetings.
In July 2022, they claimed a first series win over the All Blacks in impressive fashion, laying down a marker for this World Cup.
"Having lost the series to Ireland last year, I'd be wanting to play this game, get the chance to turn the dial back your way," former flanker McCaw said.
"What a great opportunity to do it in a quarter-final.
"I don't think it's revenge but you don't want to waste an opportunity to put things right," he added.
As well as Ireland and second in the world New Zealand the other two sides in the top four also meet this weekend in Paris in the last eight.
On Sunday, hosts and second in the rankings France face third-placed South Africa.
"They have the potential to go all the way," McCaw said.
"There are four or five who have the potential.
"Even the four in South Africa, France, Ireland and New Zealand but there are two that are not going to be here on Monday.
"That's cruel but that's the World Cup."
