The controversial incident drew the ire of Tigers coach Damien Hardwick, who described the non-referral as a "joke".
On Saturday, the AFL admitted the umpires should have called for a review.
Newly appointed AFL head of football operations Mark Evans will also speak to the umpiring department about their positioning on the goal line.
"The question is, should the (goal) umpires continue to stand in that position, because that's where they are currently coached to stand," AFL media manager Patrick Keane told AFL.com.au on Saturday afternoon.
The confusion around Friday night's decision was based on the fact Tiger forward Matt White's attempt at goal - when his side trailed by two points with three minutes remaining in the final quarter - was impeded when it struck the goal umpire.
It appeared as if the ball may have travelled through the goals, but the Sherrin struck the goal umpire in the field of play as he tried to scramble into position
In the AFL's official law book, it states: 'if the football touches an umpire or any official and does not pass over the goal or behind line, the football shall remain in play.'
However, if the ball struck the goal umpire and crossed the goal line, then the result would have been a goal.
Therefore, White's shot - which hit the umpire and rebounded back in to the field of play - was a live ball until Fremantle midfielder Stephen Hill walked the ball over the line for a behind.
"It was [Richmond's] view that the ball was already over the line when it hit the umpire. So that's why our view was that the umpire should have taken the chance to check if that was possible to know (if the ball was over the line)," Keane said.
In this instance, the goal umpire's signal was the correct one, although his positioning was questionable.
Ben Guthrie is a reporter for AFL.com.au. Follow him on Twitter: @AFL_BenGuthrie