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 and fellow players seemingly urging him to come off.
Tottenham manager Andre Villas-Boas took responsibility for the decision after the match, claiming "there were enough signs" Lloris should continue.
Luke Griggs, spokesperson for Headway, said in a statement: "We are hugely concerned that a professional football club should take such an irresponsible and cavalier attitude to a player's health.
"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."
Villas-Boas praised Lloris for his character after the game.
"Hugo seemed assertive and determined to continue and showed great character and personality. We decided to keep him on based on that," said the Portuguese.
Yet Griggs added: "Guidelines from both Headway and the National Institute for Health and Care Excellence (NICE) state people should not play any contact sport for at least three weeks after suffering a concussion.
"Sports science has evolved significantly over the past decade and yet we're still faced with the antiquated concept that a player should be brave and try to continue at all costs.
"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.
"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."
