Going into the game with one of the most intimidating attacking formations in the business, with Messi joined by Sergio Aguero, Gonzalo Higuain and Angel Di Maria, Argentina were scrappy going forward and left gaping holes in defence.
The 'Fab Four', as the quartet is known, looked more like a hastily assembled tribute act that were completely out of tune for most of the game and their 1-0 victory was barely deserved.
Higuain and Aguero managed only one shot each in the entire game compared to Messi's six.
"We have to have a good look at what happened and try to improve. We have a few causes for concern," head coach Alejandro Sabella told reporters.
One of those areas is Argentina'a work down the flanks with Aguero and Di Maria, whose combined worth is several times more than that of the entire Iranian team, proving completely ineffective against their unheralded opponents.
Higuain's own effectiveness as a striker was also brought into question with Sabella taking him and Aguero off late in the game in an effort to revive his front line.
Despite a crowded defence and three or even four Iranians marking Messi in midfield, the ball was circulated out to the wings far too infrequently.
Against tougher defences later in the tournament, their work will only become that much harder.
"We did go down the one side but we did not do it that well over both wings," Sabella said.
The Argentines also need to improve at the back with central defender Ezekiel Garay repeatedly caught off guard when Iran broke forward, especially in the second half.
Garay had laughed off suggestions before the tournament the Argentine defence was their weak link but that was exactly the case against Iran, who could have scored in a strong second half performance and stunned the two-time World Cup winners.
Iran's Reza Ghoochannejhad almost stole in with a header on one of their quick counter attacks with Garay out of position, and Ashkan Dejagah repeatedly sprinted past defender Pablo Zabaleta to carve out a few more chances for the Asians.
"We know we are not playing as well as we are expected," Messi said. "But as we go along in the tournament, we will be improving and we will reach our full potential."