The Australia fly-half endured a torrid match behind a back peddling pack at Eden Park as the Wallabies surrendered control of Pool C.
Ireland should now secure an easier quarter-final against Wales and Cooper feels they can make a real impact in the tournament.
"It was a tough game. The Irish forwards played well and they got a lot of pay out of it," he said.
"They didn't surprise us. We knew how well they can play and how physical they were. They showed that.
"They definitely lifted themselves because they were playing us, but at the same time they played some great rugby.
"If you get momentum and are always on the front foot then nine times out of 10 you'll win the game.
"Ireland are a very, very good side, a quality team. They should go well.
"The way they played against us shows they'll be a force to be reckoned with in this World Cup."
Cooper is refusing to hit the panic button, claiming it is still early days for the Tri-Nations champions.
"Our next two games are now going to mean a hell of a lot. We have to pick ourselves up and dust ourselves off," said Cooper.
"It's still very early in the tournament, all this does is make the road a little bit tougher."
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