Katie Zelem was penalised for handball despite the ball clearly hitting her head in Sunday’s 1-1 draw at Reading.
Midfielder Fara Williams scored from the spot to earn the Royals a point.
“We’ve questioned the quality of officials, we have done for many a year,” said Brown-Finnis.
She told The Women’s Football Show: “Apparently it’s been addressed but this incident highlights maybe the question needs to be raised again.”
Brown-Finnis, who played for Everton and Liverpool, called the decision from referee Kirsty Dowie “unbelievable” and “unreal”.
Last month Manchester United manager Casey Stoney said she does not want video assistant referees introduced in the WSL, while for the first time this season officials are subject to the same analysis used in the Premier League.
“I will keep harping on about referees until it’s improved because we’ve got a professional game and amateur referees, it doesn’t work,” former England defender Stoney told the Telegraph after Sunday’s match at Adams Park.
“Why do we bother going into that much detail, putting that much into the players, the players working so hard when we come here and that’s what they get and that’s the level of performance from the referee? The players deserve more.”
“At this level that’s not a mistake you should be making as a referee.”
United keeper Mary Earps said the decision had “robbed us of two extra points”.