The Irish beat the Tri Nations champion 15-6 in the biggest upset of the tournament so far in their second-round Pool C match on September 17.
The epic try-less tussle at Eden Park is likely to pit the only two countries to have won two World Cups - Australia and South Africa - into a quarter-final meeting in Wellington on October 9.
Cooper said lessons were learned from the defeat.
"The best thing we got out of it was that you have to prepare properly for each game - that's how serious the World Cup is," he said.
"It does help the mood of the team in that you don't get complacent and you realise there might have been areas in our game that we'd brushed over.
"The Irish showed us that you can't take any game lightly - not that we took them lightly - and you have to give respect to all the teams."
The 23-year-old New Zealand-born Cooper said he relished the highly-charged atmosphere and emotion of the World Cup.
"The crowd support shows us that as well, with the number of Irish supporters who were in the stands," he said.
"They really turned out and showed the World Cup passion. It is not just a one-off Test - the World Cup is a massive occasion and everyone has to be up for it."
Although Cooper has become the New Zealand public's number one enemy after two incidents involving All Blacks captain Richie McCaw, the 2010 Australian Super Rugby Player of the Year winner is not bothered by the hostile reception he has received.
"It is what it is. The support we've had everywhere we've gone as a team and personally even has been amazing," he said.
"We've just spent a few days in Hanmer Springs and every local has come up to have photos taken and wished us all the best.
"The amount of people who came to watch us train has been amazing. We've been enjoying the whole package of the World Cup and hopefully it will just get better and better."
Australia - who play Russia in their final pool match on Saturday - may have a psychological advantage against the Springboks if they do clash in the quarter-finals, with the Wallabies winning both their Tri Nations matches this year.
"You look at history like that and to some degree it gives you confidence, but it just shows against Ireland again because we beat them the last time we met then they knock us off second game into the World Cup," he said.
"I don't think history is going to play too big a part in it. The fact we play each other so often means both teams will know one another inside out and will come well prepared for what I'm sure will be one tough game if we're lucky enough to be there."
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