The Wallabies led 20-11 at the interval as they looked to postpone the All Blacks' retention of the trophy, but a second-half comeback completed a 34-27 win in Auckland to also wrap up a Bledisloe Cup clean sweep.
Henry said: "The boys played really well. A great Test match. To get the two trophies as well, we're delighted.
"We gave them a couple of tries, but at the end of the day you've just got to take your hats off to them. They played well.
"There were a couple of things we don't want to see, a couple of things, so there might be a couple of citings from this game.
"But we just got 'out-physicalled' and we just had to take that part of the game over."
All Blacks captain Richie McCaw came in for particular attention from the Wallabies, most notably Australia wing Lote Tuqiri, but explained it was just part of the game.
He said: "They gave me a tickle up. I expected a bit of attention, sevens [his number] always do.
"It was pretty physical and they were desperate at the breakdown to make their presence felt. But it is nothing I didn't expect and nothing I haven't had before."
Meanwhile, Australia coach John Connolly admits his players still have a lot of work to do in order to match the New Zealanders, even though there was often little to choose between the two sides.
"We are tremendously disappointed but are proud of our effort," Connolly said.
"We know it was in our grasp. There was no lack of effort or determination. We are working hard and going forward.
"We have a fair bit of confidence that we are not far away. The All Blacks are slightly better at the moment but we are hot on their heels."
New Zealand will now head to South Africa for their final two Tri-Nations matches.