The result now sees New Zealand and Argentina both on six points in Pool B, although the Black Sticks hold an advantage with a better goal differential.
Head coach Colin Batch said the difference in the game came down to Argentina's success from penalty corners.
"If you look at the facts they scored three of four penalty corners and we got none out of three, so obviously the game was won in those areas," he said.
"Our first half was quite good, we created two very good chances and they defended well to their credit. It would've been nice to score that goal and go into halftime up 1-0 which could have really changed the game.
"We feel a bit disappointed in our final 15 minutes, we got to 1-1 and then pushed for a victory but unfortunately conceded two more penalty corner goals."
The Black Sticks Men now move on to a crucial game against Germany on Sunday at 8:30pm (NZ time), with live coverage on SKY Sport 2.
Meanwhile, the Black Sticks Women face a must-win match against Japan on Sunday at 3:30am (NZ time), which will also be broadcast live on SKY Sport 2.
In other men's Pool B matches later today Korea go up against South Africa before the battle of the border when Germany face up to the Netherlands.