Carlos Queiroz's team defended resolutely throughout the Group F encounter and posed a threat on the counter-attack in the second half as they went close to a huge FIFA World Cup shock in Belo Horizonte.
But Lionel Messi produced a magnificent strike in injury time to snatch a 1-0 win and book Argentina's place in the knockout stages.
Nevertheless, following a lacklustre effort in their opening 2-1 win over Bosnia-Herzegovina, concerns remain over the form of the South Americans.
Sabella sent his men out in an unfamiliar 3-5-2 formation for a first-half showing that failed to catch fire against Bosnia, before reverting to 4-3-3 from the start against Iran.
"We are looking to get the balance, it is not easy," Sabella said. "It was a tough game. Iran (played) a great game and had their chances in the second half.
"I want to congratulate the guys who made a great effort, and Iran, who played a good game
"Messi was very strong and he persevered. His had attitude (is to) always look for the goal."
Messi, who also scored a sublime finish against Bosnia, echoed his manager's thoughts by suggesting that there is plenty of improvement to come from Argentina.
"Luckily, we were able to win in the end and got the points," he told reporters.
"Iran closed down well and we struggled to find space.
"We have to keep improving. We are the first to know that the level of play is not what we (can) give."
