The Swans were penalised after the steward believed Dan Hannebery had become their 19th man on the field during the third quarter.
A free kick and 50m penalty were subsequently paid to the Blues, who had just scored a goal through Eddie Betts.
The ball was handed to Carlton's back-up ruckman Setanta O'hAilpin and he kicked another major from 40m out, giving his team a seven-point lead at a crucial part of the game.
In a statement released on Monday, the AFL said: "The review of down-the-ground footage has shown that the free kick was incorrectly paid against the Swans.
"The club had three players leave the field as Carlton’s Eddie Betts was preparing to kick for goal, of which two were replaced by the time he had kicked for goal.
"The Swans still had five players off the ground at the time Betts kicked the goal and therefore player Dan Hannebery was entitled to come on the ground at the time he did.
"The umpiring department contacted Swans coach John Longmire and football manager Dean Moore … to inform them of the outcome and incorrect decision and to apologise for the error."
