Heimir Hallgrímsson has managed to drill into his side the ethos of not knowing how to get beat. And that is built of the solid foundation of relentless defensive doggedness. While Argentina were concerned with keeping all of the ball, the minnows were only concerned with their shape.
Iceland were not interested in playing the offside trap as they probably figured that the pace in the opposition ranks greatly overpowers the pace of their back-line. With a less than 100% captain in central defensive midfield, the newcomers were far more comfortable with all men behind the ball, with all of the Argentina side in front of them.
They never gave them the space to run in back loaded the box with numbers in defence, and were quick to close down any threat that arose from Messi getting onto the ball. In fact, even Angel di Maria and Kun Aguero were rendered useless for the fair majority of the game.
Inspite of Argentina camping near the opposition penalty area, the superiority in numbers for Iceland meant that Argentina never really had a decent chance or an opening. Their levels never dropped and a lot of credit needs to go into the work put in by the team in the training sessions.