The 27-year-old was unavailable to manager Alan Pardew after the Senegal Football Federation, with the support of FIFA, invoked the governing body's five-day rule following his failure to report for international duty in midweek because of a back injury.
Cisse said: "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 released a statement which said they were "dismayed and angry" at the situation and voiced the opinion that they may be being punished for refusing to allow Cisse to represent his country at the Olympic Games earlier this year.
A Newcastle United statement said: "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.
"The club is disappointed, although not in any way surprised, that FIFA has disregarded its submissions and valid points in relation to this matter and instead have supported a national association which ignored repeated attempts by the club to engage with them and, furthermore, insisted on a course of action which would have had a detrimental impact on the player's physical condition.
"The club understands that in addition to Papiss Cisse and Demba Ba, a number of other players were withdrawn from the Senegal squad. To the best of our knowledge, Papiss Cisse and Newcastle United are the only parties that the national association has sought sanctions against.
"It is the club's genuinely-held view that the Senegalese Federation have an agenda against Papiss and/or Newcastle United, possibly as a reaction to the club's decision earlier this year not to allow Papiss to participate in the London Olympics 2012.
"The club intends to take this matter up with the Football Association and any other relevant body 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)."