It gave Henry his first win in South Africa as All Blacks coach but he was not satisfied, claiming his players did not perform to their best because of the altitude.
"We're delighted with the win and we're obviously delighted with the way we played. There is a satisfaction in that," Henry said.
"But we struggled with the altitude and we will definitely be better next week when we have acclimatised better. There will be no excuse next week.
"We were happy with the win because our loss here last year in Cape Town had played on our minds a bit and it is good to put that to bed."
The Boks started well, going 11-3 up after 10 minutes, but the All Blacks stormed back, with imperious fly-half Dan Carter booting 20 points and four of their tries coming in the second half.
"We took some time to get used to the conditions," Henry explained.
"And when we got accustomed to that, we played superbly. We got the ball wide and took a huge advantage from that."
South Africa coach Jake White, who saw his side slip to a fifth successive defeat, was at a loss to explain how they fell away after such a promising start.
It needed two late tries from Jaque Fourie to make the scoreline easier on the eye for the hosts, who also touched down through Fourie du Preez.
"I am disappointed," he said. "The most important thing that we need to look at is why we made a good start and didn't capitalise on that. I really couldn't understand why we gave them so much room.
"There were times near the end of the game that we played better than at the beginning. We made mistakes and against a team like the All Blacks, they will punish you, like they did today. You can't stop praising them for the way they played."
The All Blacks paid a high price for the victory, losing prop Greg Somerville to an Achilles tendon injury and he could be sidelined for around six months.
Back-row forward Chris Masoe (ankle) and full-back Leon Macdonald (hip), meanwhile, both look set to miss next week's game, while Reuben Thorne has a suspected broken thumb.