Cavani was suspended for three matches and fined £100,000 for posting a message in response to an Instagram story after he scored twice in United's 3-2 comeback win at Southampton on 30 November (AEDT).
The post from Cavani featured a Spanish word often used as a term of endearment in Latin America, with Cavani later apologising and deleting when he is said to have become aware the word could be construed as having racist connotations in English.
An FA investigation, which involved a language expert witness, concluded that Cavani's actions constituted an aggravated rule breach, because the language used "included reference, whether express or implied, to colour and/or race and/or ethnic origin".
On Tuesday (AEDT), the Uruguayan Football Players' Association (AFU) issued a statement, shared by international stars Diego Godin and Lucas Torreira, that called the sanctions against Cavani "reprehensible", while accusing the FA of displaying a "biased, dogmatic and ethnocentric vision".
South American football's governing body was not so fiery in its own statement, but it similarly suggested the FA had not taken "cultural characteristics" into account.
"CONMEBOL expresses its solidarity with the player Edinson Cavani, punished by the English Football Association," the statement read.
"The disciplinary action of the outstanding player of the Uruguay national team clearly does not consider cultural characteristics and the use of certain terms in everyday speech in Uruguay.
"The judgement of these types of statements, within the framework of a process that can lead to penalties for the athlete and affect his reputation and good name, must always be carried out taking into account the context in which they were made and, above all, the cultural peculiarities of each player and each country.
"CONMEBOL condemns and will always condemn with the greatest energy any racist or discriminatory instance, but the specific case for which Cavani was sanctioned does not constitute one of these."
Cavani, who must also undergo a face-to-face education course, accepted his FA ban but insisted his "heart is at peace" over the social media post.
The 33-year-old sat out United's 2-1 Premier League win over Aston Villa last weekend and will also miss Thursday's (AEDT) Carabao Cup semi-final showdown with Manchester City and the FA Cup third-round tie at home to Watford.