The Albiceleste midfielder collided with Georginio Wijnaldum when competing for a header during his side's semi-final win over the Netherlands, playing the entire game despite appearing severely dazed after the incident.
Uruguay's Alvaro Pereira suffered a similar injury against England earlier in the tournament and Headway expressed concern at the fact both players were allowed to continue playing, calling on Fifa to enforce their guidelines on the issue more rigorously.
"On a big stage like the World Cup, it's incredibly hard to understand how there could be two different players throughout the course of a tournament who have been allowed to continue when they have seemingly been knocked out or suffered a concussive injury," a Headway spokesperson told Perform.
"There needs to be some very serious questions asked of Fifa for how they have allowed this situation to happen.
"The Fifa guidelines suggest that if a player suffers a concussion or if there's a risk of concussion a player should be taken from the field and not allowed to return."
The health campaigners drew comparisons with another incident that ocurred in last season's Premier League, where Tottenham Hotspur keeper Hugo Lloris stayed on the pitch despite being concussed in a clash with Romelu Lukaku, urging Fifa not to endanger players' wellbeing.
"That's Fifa's own guidelines and if you look back to the Hugo Lloris situation, you had Fifa executives coming out and saying these sorts of things," their representative continued.
"Yet on the biggest stage - the FIFA World Cup semi-final - you have a player that is clearly in distress seemingly being allowed to overrule the doctors and return to the field.
"It cannot be that a player is can make that decision - it has to be a medical decision and [doctors] have to be given the power to overrule both players and managers."
World Footballers' Association FIFPro also asked Fifa to take action following the Pereira incident - asking football's governing body to "conduct a thorough investigation into its own competition concussion protocol."