Carter, whose late drop goal broke Ireland's hearts in last week's 22-19 defeat, suffered a hamstring injury in training and will be replaced at fly-half by Aaron Cruden for the third Test in Hamilton this weekend.
However, the All Blacks won the World Cup despite losing Carter for much of the tournament and O'Driscoll expects Chiefs star Cruden to seize his chance in the starting line-up.
"They managed okay in the World Cup, didn't they?" he said.
"Dan Carter is a world-class player but Aaron Cruden is handy enough and he has shown it. The bits I've seen of the Super Rugby this season he has been pretty impressive.
"They have to look at life without Dan Carter and it gives Aaron a great opportunity. It is not all about the guy pulling strings at 10, you need smart players around you and I think New Zealand have that."
While the hosts are without their star man, Ireland will be at full strength after the return to fitness of Keith Earls.
The Munster flyer will line up on the left wing, with Paddy Wallace partnering O'Driscoll at centre and Peter O'Mahony taking Jamie Heaslip's place at number eight.
The starting line-up is otherwise unchanged from the side that came within 35 seconds of securing a draw with the world champions last week.
Wallace is O'Driscoll's third different midfield partner in the three-Test series, but the skipper has no doubts over the Ulster player's capabilities.
"Any time you have someone like Paddy coming in, he will always bring something," he said. "Not just his playing ability but the character he is around the squad.
"I've known Paddy a long time, played underage level with him, under-19s, through college and through senior rugby with Ireland.
"Knowing the type of professional he is, the shape that he has kept himself in, Paddy will do an excellent job. I'm looking forward to reigniting that midfield partnership with him."
Coach Declan Kidney admitted that it was "not ideal" that Wallace only arrived on Tuesday evening, but he feels the coaching staff have allayed any jet-lag concerns.
He said: "Paddy has always been a great player for Ireland. We talk about the squad ethic and what Paddy has given in the background, and in his 10 years' service to the Irish team, has been fantastic."
On Earls, he added: "Keith's stated preference is he prefers to play at 13 but Brian (O'Driscoll) is not one to give it up too easily.
"He is a great team player and he is happy to be back in. He has rehabbed quite well, which is a credit to the medical team and himself for getting over (his shoulder injury). He has trained well this week."
Kidney feels Ireland need to show that their rousing performance in the second Test was not a once-off or slip back to the levels displayed in the 42-10 loss in Auckland.
"Last week is over," he added. "New Zealand are well capable of doing to us what they did at Eden Park again. That fear needs to be within us, to know that it can happen unless we turn up, do our job, and do it to the best of our ability.
"We need to do that and add on that extra 10% that we didn't have last Saturday."
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