Vertonghen was left bloodied after he collided with team-mate Toby Alderweireld when they challenged Ajax goalkeeper Andre Onana to an aerial ball in the first half of Spurs' 1-0 home defeat in the first leg on Tuesday.
The 32-year-old received lengthy treatment before being cleared to return to the pitch, only to signal moments later that he was unable to continue.
"I wasn't involved, it was the doctor's decision."— Sky Sports News (@SkySportsNews) May 1, 2019
Mauricio Pochettino says @SpursOfficial followed concussion protocols after Jan Vertonghen was allowed to return to the field after a head injury in Tuesday's Champions League defeat to @AFCAjax: https://t.co/GTXKxs7X2n pic.twitter.com/jwlLx98N4i
Vertonghen appeared groggy and had to be helped down the tunnel in worrying scenes but stated after the match he had no concussion despite fainting.
However, Headway spokesperson Luke Griggs believes a rule change is needed to allow players involved in such incidents to be assessed thoroughly without their team being disadvantaged.
"It is hugely disappointing that we are once again talking about concussion rather than the game itself," he said.
"Concussion is notoriously difficult to diagnose. The symptoms may be hidden and require the individual to be honest about how they’re feeling, while they can also be delayed in their presentation.
"Assessing a player for three minutes – or even five, as was the case with Jan Vertonghen – does not allow for medical staff to make a reliable diagnosis, particularly when this is conducted on the pitch under the gaze of tens of thousands of fans eager for the game to resume.
"The pressure on club medical staff is enormous and unfair, particularly in such high-stakes games such as a Champions League semi-final.
"We believe the time has come for football to introduce temporary concussion substitutions that would allow for longer off-pitch assessments to be conducted.
"In addition, independent doctors with expertise in concussion and head injuries should make the ultimate decision as to whether or not a player is fit to continue.
"Not every head injury will result in a concussion. But allowing players to continue while showing clear signs of discomfort following a head injury is contrary to the 'if in doubt, sit it out' principle at the heart of all effective concussion protocols."
Tottenham boss Mauricio Pochettino defended the club's doctors in light of criticism following the incident.
"Our medical staff followed the protocol and they decided it was possible to restart the game and possible for Jan to play again. But, of course, Jan started to feel unwell and we needed to change him," Pochettino said.
"Of course, I was worried. That is normal because for me the most important [thing] is the health of the player. If they say to me 'change', I am not going to doubt that. In that type of situation, the medical staff are the bosses. Never am I going to question them."