The Irish coaching team will prepare the squad to guard against the danger of wilting against the All Blacks, who were criticised by their national press after a sub-standard performance on Saturday in Hamilton.
Even All Blacks coach Graham Henry described his team's effort as "rusty".
Given the way the All Blacks finished the match, pulling clear to win 34-23, and judging by the expectation they will improve on Saturday, Ireland face a searching examination of their ability to mix it with the World Cup favourites.
"It will be tougher next week," said O'Sullivan.
"New Zealand will be better, and we will too. But we will have to be. That's the challenge for us to take up."
Ireland were 16-8 ahead at half-time, thanks to Brian O'Driscoll's converted try and three penalties from the boot of Ronan O'Gara.
They were pinned back by a touchdown from Mils Muliaina early in the second half, but then Ireland replied in kind when Andrew Trimble gave them a 23-15 lead.
A first victory in 101 years for Ireland against New Zealand was in sight, but Ireland conceded three penalties to Luke McAlister and Troy Flavell crossed late on to seal a home victory.
"We were consistently pinned back and having to defend for long phases," added British & Irish Lions coach O'Sullivan.
"There was an element of fatigue but I think it was from just slugging it hard in the trenches for so long.
"New Zealand held onto the football for long phases and just kept running at us making us make hard tackles.
"We couldn't create those beachhead positions to work on.
"To be fair to them, they held onto the ball and kept coming at us, coming at us and coming at us and made us work very hard.
"We were a bit punch-drunk at times but that tends to happen in football. Every tackle was a bone-shaker. They did wear us down."
Captain Brian O'Driscoll balked at the description of Ireland as 'plucky'.
"I think we were more than plucky," the Lions skipper said.
"I think we had them worried, and rightly so.
"We gave as good as we got for a fair proportion of the game.
"This team is about being a hell of a lot more than plucky.
We've come on a huge way in the last few years and we don't accept mediocrity.
"We've got two big performances left on this tour and we'll just have to go hard at Eden Park next week and lift our game 15% and be there in the 80th minute instead of falling way in the 63rd or 64th minute."