Opponents Jordan were awarded a 3-0 win and Iranian officials said the decision could cost them a place in the 2012 Games.
FIFA said both teams had been reminded before Friday's match about its rules and that, as a result, Jordan had decided not to select several players.
"The match commissioner and match referee therefore decided to apply correctly the Laws of the Game, which ended in the match being abandoned."
"We made the required corrections and played a match afterwards," Farideh Shojaei told Reuters TV in an interview.
"We played the next round and were not prevented from doing so, and they didn't find anything wrong. That meant that there are no obstacles in our path, and that we could participate in the Olympics."
FIFA's rules for the 2012 Olympics state: "Players and officials shall not display political, religious, commercial or personal messages or slogans in any language or form on their playing or team kits."
Shojaei added: "In reality, this kit is neither religious, nor political, nor will it lead to harm to a player. "
She said the ruling meant the team were now unlikely to qualify for the Olympics.
"The countries that invested, and spent money and time and took part in the second round will clearly not be willing to repeat these games, especially if this week it becomes clear which team will enter the final round. So it is extremely unlikely."
(Additional reporting by Sanam Shantyaei in Tehran; Writing by Clare Fallon; Editing by Alan Baldwin)