Despite playmaker Cooper making several errors against South Africa, Australia prevailed, posting an 11-9 victory that booked a semi-final appointment with New Zealand at Eden Park next Sunday.
"I can only talk about experiences that we've had with them, and he (Cooper) has played pretty well against us," former Northampton boss Smith said.
"He is mercurial, he is dangerous. If he has a real good day then you are in trouble, so we've got a lot of respect for him.
"People probably say the same thing about any player who has a bad trot.
"We had an experience with Zac Guildford (All Blacks wing) for example, who had a poor game before the World Cup, got a chance in the World Cup and then had a blinder.
"Quality players come right pretty quickly."
New Zealand have welcomed Bath-bound number 10 Stephen Donald and wing Hosea Gear into their squad as respective replacements for injured pair Colin Slade and Mils Muliaina as they look to reach a first World Cup final since 1995.
And Smith insists it is business as usual ahead of New Zealand's biggest game in the tournament.
"Any time you get to this stage in any tournament, whether it be Super Rugby, Premiership, Heineken Cup, World Cup, it is about will. It is about the strength of your will," he added.
"Tournaments throw up all sorts of things at you - injuries, selection - and you cannot control any of that, and it's the same for the other team.
"It is not who you've got in the team, it is what you've got inside you that counts at this point, and that is what will win it.
"I don't think you can make any assumptions about them (Australia).
"We've got huge respect for them, and I am sure they've got great respect for us.
"We've played each other often over the last few years. We know them well, they know us well. We know it's going to be a massive encounter."
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