New Zealand held a 10-6 lead at half time after a Joe Rokocoko try in the 10th minute, but had to withstand a determined attacking barrage from the Wallabies in the second half.
McCaw in particular was truly inspirational, stopping one certain try with his defence and forcing a number of crucial turnovers.
"You can't play any better than that," Henry said of McCaw's performance. "I thought he was outstanding - the outstanding individual performance of the game, superb."
A modest McCaw said the backs-to-the-wall victory ranked among the best he has been involved in and heaped praise upon his team-mates for their great defensive display.
"It would be right up there," the openside flanker said after the match.
"I think it just displayed that defence wins Test matches. We put a lot of effort into that and I am pretty proud of the guys how they dug pretty deep.
"Whenever you play the Wallabies, it is physical and the ball gets chucked around a lot."
The All Blacks dominated most aspects of the game but their line-out suffered in the second half as they handed the Wallabies a glut of possession.
Subsequently, the Australians launched wave after wave of attack, spending the final quarter of the game camped in New Zealand's 22.
"I know all our guys are out on their feet - the last few minutes we had to dig pretty deep," said McCaw.
"It makes it all worthwhile when you get out on the right side of the scoreline."
New Zealand now have a weekend off while the Wallabies face South Africa in Sydney next Saturday.