Williams was dazed and fell to the floor after blocking Marcus Rashford’s powerful 24th-minute shot with the top of his head.
The Nottingham Forest defender continued for another 12 minutes before sitting on the turf and receiving treatment again, before being eventually replaced by Connor Roberts in Wales’ 3-0 defeat.
Brain injury charity Headway criticised the handling of the incident, saying “yet again medics are giving no options” while calling for the introduction of a temporary concussion rule.
Wales manager Page said Williams had been allowed to continue after initially passing Fifa’s concussion test.
He said: “Neco took a blow to the head, so there are protocols in place understandably with concussion. He passed the initial test.
“We followed the Fifa guidelines. The Fifa doctor OK’d him to stay on the pitch, but he was advised if there was any symptoms then to flag it up straight away, and that’s what he did.
“There was no second thoughts at all, he was off straightaway. We’ve covered all the protocols and the FIFA guidelines.”
Headway, however, responded to the incident by tweeting: “YET AGAIN medics are given no options! A temporary concussion rule would have not resulted in Nico (sic) Williams being left on the pitch after #concussion. How many more?!”
Former England captain Alan Shearer, working as a television pundit on the game in Doha, backed Headway’s call for the immediate introduction of temporary concussion substitutions.
Shearer told BBC One: “I would say to IFAB, ‘what on earth are you waiting for?’ because everyone is under pressure then to make a decision.
“You’ve got the doctors and the physios on the pitch trying to buy a little bit of time.
“If they were able to get him off for 10 minutes, assess him, bring someone on and then make their mind up there rather than be put under huge pressure on the pitch (it would be an improvement).”
Williams’ injury was another sad chapter in Wales’ miserable World Cup finals story, their first for 64 years.
Wales produced flat performances in drawing 1-1 with the United States and losing 2-0 to Iran, and then failed to lay a glove on England as an early departure from Qatar was confirmed.
Star duo Gareth Bale and Aaron Ramsey were both well below their high standards, with the former managing just seven touches and one completed pass before failing to reappear for the second half because of a hamstring injury.
Page said: “We’re disappointed because we know in a couple of the games we haven’t shown our true colours. That is probably the most frustrating thing for me and the group of players. They know that themselves.
“I don’t need to tell them that. It’s important we learn from it. We’ve had a taste of it and we want to continue to qualify (for major tournaments).”
Wales start their Euro 2024 campaign away to Croatia in March, with Armenia, Latvia and Turkey also in their group.
Bale, now 33, said after the England defeat he will “keep going as long as I can and as long as I’m wanted”, but the squad will naturally evolve for the Euro qualifiers.
Euro 2016 survivors Chris Gunter and Jonny Williams, now both playing for League Two clubs, may have reached the end of the international road.
Young midfielders Jordan James and Ollie Cooper – who were both on standby in Qatar – and Fulham’s highly-rated teenager Luke Harris are set to be involved for the opening Euro 2024 qualifier in Split.
Page said: “We’ll have a look at the squad, at the players we’ve got. If there are young players out there that we need to push and promote, now’s the time to do it.”