The All Blacks also had to contest the final five minutes of the game with only 13 men after yellow cards for backs Leon Macdonald and Sam Tuitupou.
The former Wales and British and Irish Lions coach told Sky Sports: "We scored three tries to one, I guess the people at home were on the edge of their couches.
"They put on a lot of pressure in the forwards, we didn't function particularly well there, but we did get three tries to one and we probably blew a couple of opportunities to take it out of being tight. It shouldn't have been tight in the finish.
"We're pleased. The boys played with plenty of character and got through. But we've got plenty of work to do ahead of the Tri-Nations, obviously."
The Pumas' tight-knit side, fresh from defeating Wales, were quicker into the game than the All Blacks, many of whom had taken four weeks off after the Super 14 finals.
Henry defended his decision to use a completely different starting XV from the Tests against Ireland, but qualified that by claiming there was much work to do.
"There's always risks in the strategy," he said. "The idea was to let them recover and recondition, not rotate, so they came back well.
"The game will be good for them coming into the next one.
"We've a lot of work to do. We're nowhere near it yet. But hopefully the guys are fresh and they're raring to go."
Henry and the party return to New Zealand ahead of naming his Tri-Nations squad this week, with the competition curtain-raiser coming on July 8, against Australia in Christchurch.