Nearing the end of the pool stage, Michael Cheika's Wallabies have just two tries against them - the tournament's equal best.
Ever the perfectionist, Grey is demanding more from his charges as they approach the competition's knockout stages.
"We're trying to ramp it up from the England game looking into the Wales game," Grey said.
"That's where we need to look for those little improvements defensively and from an attacking perspective.
"We need to attack better than we did, we need to defend better.
"You're never happy leaking points.
"It's more the process of the way we we're going about defending, which has been impressive.
"The guys are really fighting for each other.
"We leaked a fair few linebreaks against England, but our scramble was really good.
"We need to continue to improve each week and we've already spoken about that from the England game looking into Wales and the threats they pose.
"They're going to stretch us, they play the ball to the width a lot and look to capitalise.
"We want to be able to put pressure on the opposition with the ball and without the ball.
"The players really drive their standards around that defensive pressure.
"You do have to have the technique, but having the will and the intent certainly goes a long way to getting the job done."
Tries conceded by teams to have played in every World Cup:
Australia: 41 tries in 47 matches
New Zealand: 55 in 49
Ireland: 57 in 36
Argentina: 60 from 36
England: 61 in 46
Scotland: 61 in 46
France: 73 in 49
Wales: 74 from 38
Excluded:
South Africa: 29 from 35 (did not compete in 1987 or 1991 WCs)