The replay of Carlos Tevez's opening goal from a clear offside position sparked a melee during the game and at half-time rival substitutes squared up to one another behind the Mexican bench.
"This shouldn't happen," FIFA spokesman Nicolas Maingot told a news conference. "Replays can be shown but not when there are controversial situations. We will work on this and be tighter in future."
"It has worked so far very well. Last night was a mistake. It should not happen again," he added, declining to answer numerous questions on the contentious decisions made by referees and FIFA's rejection of goal line technology.
In another questionable decision that angered English fans on Sunday, England were denied an equaliser in their match against Germany when a shot from Frank Lampard hit the crossbar and clearly bounced behind the goal line.
FIFA is under increasing pressure to allow goal line technology or an extra referee behind the goal line to assist in such situations.
Spanish striker Fernando Torres said steps were needed to stop mistakes by officials altering the course of matches.
"We're tired of asking for technological help for these kinds of situations because they can determine something as important as whether you get knocked out of a World Cup," he told a Spanish radio station.
FIFA president Sepp Blatter has rejected goal line technology, saying he wants football to be played under the same rules at all levels and retain its human element.
