Cisse was stopped from facing Swansea City because of FIFA's five-day rule, enforced by the world governing body in support of the Senegalese Federation.
Newcastle claim they advised Senegal that both Cisse and strike partner Demba Ba would be unavailable for Wednesday's friendly against Niger due to injury.
The club say they received no reply from the Senegalese despite further attempts to contact them, only for Senegal to ask FIFA to impose the rule which was brought in to stop clubs withdrawing players from internationals without good reason.
Cisse was withdrawn at half-time against West Ham United last weekend with a back injury.
"I am deeply disappointed by the actions of my Federation which have punished me and my club," Cisse said in a statement on Newcastle's website on Saturday.
"I love playing for my country and would only withdraw from a squad - for either a friendly or competitive game - for a genuine reason.
"I am fully supportive of the position my club has adopted in this matter and am sorry that the Federation seem to doubt my honesty and integrity. I will now consider if I wish to continue to captain my country."
Newcastle were equally upset by the decision.
"It is the opinion of the club that it is wrong and wholly unjust for a national association to behave in this manner and for FIFA to endorse their stance and automatically apply the sanction without taking into account the specific facts of the case," a club statement said.
"The club is disappointed, although not in any way surprised, that FIFA has disregarded its submissions and valid points in relation to this matter.
"It is the club's genuinely held view that the Senegalese Federation have an agenda against Papiss and/or Newcastle United."
Newcastle said Senegal's attitude towards them could be a reaction to their decision earlier this year not to allow Cisse to participate in the 2012 London Olympics.
Newcastle added they would seek advice from the Football Association and other bodies within the game "to try to stop national associations/federations and FIFA from preventing an employee [a player] from fulfilling their contractual obligations to their employer [a club]."
The Premier League club stated they would also seek legal advice.
