Kick It Out chief executive Tony Burnett says the football authorities must assume "genuine responsibility" for protecting players from discriminatory abuse, on the day FIFA imposed a two-game stadium ban on Hungary.
Raheem Sterling and Jude Bellingham were subjected to monkey chants during England's World Cup qualifier against Hungary in Budapest on September 2.
FIFA opened disciplinary proceedings a day later, promising "adequate action" would be taken.
On Tuesday the Hungarian federation (MLSZ) was fined 200,000 Swiss francs (just under £160,000), which far exceeds previous penalties FIFA has issued to Hungary, but Burnett believes the stadium ban – one game of which is suspended for two years – goes nowhere near far enough.
He also criticised the football authorities over flaws in disciplinary arrangements which meant a UEFA stadium ban imposed for racist chanting and homophobic banners during the Euros did not carry over into the World Cup qualifiers, and meant FIFA's disciplinary committee could not take the UEFA ban into account when setting its own sanctions.
"Kick It Out welcomes sanctions imposed on the Hungarian Football Federation, but those announced by FIFA today unfortunately do not go far enough," Burnett said.
"The Hungarian Football Federation was already serving a UEFA ban, so we know that punishments like this do not effectively deter fans who abused England players earlier in the month from repeating their behaviour.
"We need the footballing authorities to assume genuine responsibility for player safety, both from physical and discriminatory abuse. This means applying or duplicating sanctions that result from discrimination during competitions in other federations, as well as assessing the risk posed to players during games held in specific nations.
"For those countries that have proven unable to control fans' appalling behaviour, excluding them from competing at major tournaments should not be off the table."
The UEFA sanctions do not come into force until the Nations League next year.
Article 66 of FIFA's disciplinary code allows confederations such as UEFA to request the extension of a sanction into FIFA competition, but UEFA sources insisted at the time of the incident against England that its own regulations had prevented it from doing so.
Burnett said the day after the incident that the abuse had been "preventable and predictable".
Bellingham tweeted the day after the match to say that racist abuse would be "part of the game" until "proper punishments" were issued.
FIFA said in a statement on Tuesday afternoon: "After analysing and taking into consideration all the circumstances of the case, specifically the seriousness of the incidents (racist words and actions, throwing of objects, lighting of fireworks, blocked stairways), the committee decided that the MLSZ would play its next two home matches in FIFA competitions without spectators, the second match being suspended for a probationary period of two years.
"FIFA's position remains firm and resolute in rejecting any form of racism and violence as well as any other form of discrimination or abuse. FIFA takes a clear zero-tolerance stance against such abhorrent behaviour in football."
