"I don't know why people are quizzing that selection. He's been a long-time player for Australia and I think he's done well for us," Cheika said.
"He can obviously improve like all our players can.
"I think it's just an easy stereotype to have a crack at him.
"As a coach, I evaluate what's in the game, not what's written or tweeted or whatever.
"We see some improvements we can make in him over the next few weeks that will get him playing better in our system.
"I'm really comfortable with selecting him and I don't think there was a question on it."
The 55-Test veteran Cooper is one of two specialist five-eighths in the squad along with Bernard Foley, while Cheika has Matt Toomua, Kurtley Beale and Matt Giteau who can all play No.10.
Cooper's second-half sin-binning last Saturday night all but ensured the Bledisloe Cup stayed with New Zealand.
He was shown a yellow card - for the second time of the Wallabies' winter campaign - in the 48th minute for a high shot on All Black Aaron Smith as the halfback was set to score a try.
A penalty try was awarded which gave the Kiwis their second five-pointer of the night before they crossed twice more while Cooper was in the bin.
The Queensland Reds' star copped a hammering from fans at Eden Park, continuing his frosty relationship with New Zealand crowds who booed him mercilessly during the 2011 World Cup due to his run-ins with All Blacks skipper Richie McCaw.
- AAP