Coach Ian Foster said they knew Italy would represent another step up from what was experienced earlier in the tour against the United States Eagles.
Taking time to settle down was not unusual in a Test match, but they hadn't got too loose and found some solutions to score three tries in the first half.
"Overall, [I'm] really delighted with the score, with the result, but we got a good workout," he said.
"We got put under a lot of pressure in that first 25 minutes. They found ways to slow the ball down, we tried to force our game a little bit and a lot of that was the pressure they put us under. They [Italy] probably deserve a lot of credit for the way they started that game.
"What I was pleased with was we started to tighten our game up after a few errors and applied a lot of pressure on them, mainly through our set-piece, and that worked well.
"They stayed in the game right till the end, and I think for this particular All Black team, it was a great Test match for us to have because we didn't get it our own way, and we had to find a way," he said.
The tactic of going to the middle of the park more in the second half had the effect of spreading Italy out a little more which produced more reward than earlier.
"There's no one strategy here, there's a whole lot, and you've got to be good enough to see it at the time," he said.
Foster said he was pleased with hooker Dane Coles' man of the match effort. He had given everything, scored two tries, and contributed to the leadership role in the young pack.
"We've had to make sure we grow depth because we've got players here for a long, long time and we're delighted with the progress we're getting out of that, so tonight is another good learning curve for a number of newer players," he said.
"To finish both halves in a strong manner was pleasing. Clearly, we have to work on some of our decision-making with the ball. We put ourselves into a few brick walls at times but that's ok, we'll tidy that up," he said.
Replacement halfback Finlay Christie showed he had settled into the team. Foster said he took time to settle with a couple of penalties conceded but he was courageous and hoed into everything, he was quick and with more time with the side the better he would be.
Italy coach, Kieran Crowley said his side's performance produced a line in the sand, especially defensively, and gave them something to build on.
They showed good line speed and integrity to put the All Blacks under pressure by knocking them back.
"But we must get better. New Zealand's fitness was better and they stepped the tempo up. If you can stay in the game for 65 minutes you are in the game," he said.
However, the speed of the ball they produced was not good enough in attacking situation and their set play must improve, especially defending opponents' lineout drives, he said.