Senegal's 1-0 loss to Colombia in its Group H closer meant it finished third in the final table, below Japan thanks to its count of six bookings compared to the four collected by its pool rival.
Fair play points are being used to settle groups for the first time at a FIFA World Cup, with Japan and Senegal finishing with the same number of points and identical goal difference and goals scored tallies.
Aware of the situation, Japan - for whom extra bookings could have resulted in elimination - played out the closing stages of its game against Poland at walking pace despite trailing 1-0.
And now the FSF has asked FIFA to punish teams that play in the fashion Japan did.
"In future, FIFA should penalise a team that plays that way," spokesperson Kara Thioune said.
"FIFA has adopted a new system but does the fair play rule solve all the problems? After the game, nothing happened to either Japan or Poland.
"There should be some means of penalising players, coaches or teams for such an attitude."
The FSF has also revealed that it sent two letters to FIFA on Friday, one of which addressed the fair play criteria while the other complained about the standard of officiating in the defeat to Colombia.
"The Federation believes that Japan literally refused to play when it learned that Colombia had just scored a goal against Senegal, a refusal to play that suited Japan but which is contrary to the principles governing football," the letter stated.
"The Federation is all the more shocked that the Japan coach did not deny the facts. In the post-match press conference, the latter even confirmed he had made the decision to manipulate the result by keeping the score at 1-0.
"The Senegalese Football Federation deplores the lack of fair play this Japanese team has shown. It challenges FIFA on the notion of ranking the number of cards which loses its meaning and interest when the team lacking fair play is not worried by any penalty."