Henry said: "I think it was a big improvement on how we played in the last two Tri Nations games so we are pleased about that.
"We got better as the game went on - we built better in the second half and showed a bit more patience and discipline, and the tries came at the finish.
"We looked like scoring most of the tries and we probably got a bit frustrated that we didn't score earlier, and that led to a bit more impatience and a lack of discipline.
"But I think it was a fair reflection - maybe we could have scored a couple more earlier, but I think it is a good step forward."
Sitiveni Sivivatu was replaced by Joe Rokocoko - the latter not even named in the original 22 - minutes before the start of the game, and Henry revealed that Sivivatu had injured himself in the warm-up.
He added: "Sivivatu got a twinge in his calf in the warm-up and that is why he didn't play, which was frustrating for him and frustrating for us because you train that way all week.
"But I think Joe came on and did well.
"He showed a lot of composure to come from outside of the 22 and play the way he did.
"I think a lot of questions were answered and I think there has been a lot of progress made."
Opposite number Jake White's disappointment at the loss was tempered by his delight at the effort shown by his young charges, who were written off before the game.
The South Africans were still in the match, trailing by just 12-6 when the All Blacks finally broke the shackles with a try from substitute scrum-half Brendon Leonard.
White said: "I don't think the scoreline is a true depiction of the game itself.
"I'm obviously disappointed with the last 20 minutes but I think that the bench and the 22 play a major role in rugby union.
"So I think the lesson learnt here is about the strength in depth and the impact guys off the bench can make in the last 15 to 20 minutes.
"You win games with the 22 in the squad not just the 15.
"It reaffirms my thoughts on the tour - that a lot of guys have put their hands up and made a huge impact."
New Zealand's win sets up a thrilling final against Australia next Saturday which will decide not only the Tri Nations title, but also the Bledisloe Cup.