FA general secretary Alex Horne said the sanctions did not send a "strong enough message" about racism, and that the governing body will appeal against two-match and one-match bans for Steven Caulker and Tom Ince respectively.
Rio and Anton Ferdinand also criticised the sanctions on Twitter contrasting it with an £81,000 fine and one-match ban handed to former Arsenal striker Nicklas Bendtner for displaying a betting firm's logo on his pants during Euro 2012.
Uefa's control and disciplinary body also banned four Serbian players and two coaches for scenes in October.
Anton Ferdinand said: "Wow UEFA ain't serious with their punishment... So showin' a sponsor is worse than racism and fighting!"
His brother Rio added: "Uefa are not serious at all on racism. Fines do not work at all. They have zero impact on federations/clubs/fans/players #fact."