Hansen hailed his bench for injecting energy and urgency in the second half as the All Blacks wore down their combative opponents after trailing with 24 minutes to go at Wembley Stadium.
"It took a long time to get on top," Hansen said.
"No doubt we were rusty. Really rusty. Not only that, there was some apprehension and I've seen that from every team this weekend. That's what comes with the World Cup and the first match, everyone is desperate to get started, get points on the board."
Behind 13-12 at halftime, Hansen made four changes in the first five minutes of the second half, with replacement Sonny Bill Williams providing the missing spark in the backline.
Although they fell further behind after another Puma penalty, halfback Aaron's Smith's try restored order and from then on the All Blacks, with a full complement of players back on the pitch after two yellow cards, were finally able to impose their game on their tiring rivals.
"Normally we'd go further in before making substitutions," Hansen said. "We needed more energy and urgency... the bench brought that. The bench was outstanding."
It was still far from a perfect second half from New Zealand who were not at their clinical best - notably spurning two gilt-edged try-scoring chances when winger Nehe Milner-Skudder, who has burst on to the international scene this year, and replacement forward Sam Cane fluffed their lines.
Their errors followed on from an engrossing first half when the All Blacks, having coasted into a 9-0 lead, were pressured to such an extent that captain Richie McCaw and centre Conrad Smith were forced into rash acts of ill-discipline.
McCaw, booed loudly by the thousands of Pumas fans, went for a trip while Smith was shown to the sidelines for cynical play at the breakdown, leaving the All Blacks with 13 men for a brief time.
Hansen said both cards were "pretty dumb".
"They know they were dumb ones. Sometimes in the heat of the moment you have a small brain explosion. We can't afford to play with 14 men, let alone 13 for a while."
McCaw added: "As soon as it happens you wish it hadn't. I knew straight away... it was reflex thing."
New Zealand next face Namibia at the Olympic Stadium on Friday morning (NZT) and while no one expects anything less than a thrashing, Hansen knows his team will improve.
"We have something to work on which is good but we can move on and look forward with confidence," he said.
