The France international goalkeeper was knocked out in a second-half collision with Everton forward Romelu Lukaku during a goalless draw at Goodison Park.
However, following lengthy treatment, Lloris remained on the pitch, despite Tottenham's medical staff urging him to come off, and Headway have slammed the decision to allow the 26-year-old to continue.
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"When a player – or any individual – suffers a blow to the head that is severe enough for them to lose consciousness, it is vital they urgently seek appropriate medical attention.
"A physio or doctor treating a player on pitch simply cannot accurately gauge the severity of the damage caused to the player's brain in such a setting as there may be delayed presentation of symptoms.
"By continuing to play, the player may have caused greater damage to his brain. He should have been removed from the game immediately and taken to hospital for thorough tests and observation."
Spurs boss Andre Villas-Boas said Lloris' "assertiveness" was the reason he was allowed to continue, but Headway claim that shows a complete lack of awareness for the nature of the injury.
"Mr Villas-Boas' comment that his player's determination to play on was proof of his 'great character and personality' is simply wrong and dangerous," the statement continued.
"You are not a hero if you play on after suffering a concussion; all you are doing is risking your health.
"Football has to react to this and bring in stricter measures to ensure no similar risks are taken in the future."