Kristian Nushi, who plays for Swiss club St Gallen, had to stay behind because he could not get a visa to travel to Russia for the game away to Spartak Moscow.
"We all know your support and FIFA's support to ensure the right for Kosovo football in spite of political obstruction," said the FFK in a letter addressed to FIFA president Sepp Blatter.
"It is clear however that your mediation is more than even necessary to find solutions. The injustice imposed on Kristian Nushi constitutes a dangerous precedent and demonstrates the unfair treatment of Kosovo football as well as the need to reaffirm the supremacy of sport over political criteria."
The FFK said there had been a similar case in August when two players from Albanian club Kukes, holding Kosovan passports, were refused Ukrainian visas for a match away to Metalurh Donetsk in the Europa League.
In that case, the two players took out Albanian nationality and were allowed to travel, the FFK said.
UEFA said at the time that it was aware of the St Gallen case and that, although it `tried to help clubs, it was ultimately up to the respective embassies to grant visas.
"The FFK and the whole Kosovo football community....remained shocked by the absence of reaction," said the FFK.
"This denial constitutes a clear violation based on the "national origin" of the universally respected sport of principle of non-discrimination as enshrined in the Olympic Charter, the FIFA statutes and UEFA statutes."
"This silence contrasts starkly with the positions adopted by other international federations and/or European confederations."
FFK said that the governing body of table tennis had successfully pressured Russian authorities to grant visas to Kosovo players taking part in an official championship.
By contrast, UEFA had been quick to react to reports that Kazakh club Shakhter Karagandy had sacrificed a sheep before a Champions League qualifier.
"While at the same time, a strong action was implemented to prevent animal sacrifice before UEFA Champions League matches, nothing was said nor done publicly to help a professional footballer to play for his club, and to make sure that the independence of sport over politics would be enforced."
Kosovo declared independence from Serbia in February 2008 and has been recognised by at least 100 countries including the United States and 23 of the EU's 28 members, but not Russia.
Russia, a Serbian ally and U.N. Security Council veto-holder, has so far thwarted Kosovo's hopes of joining the United Nations.
Kosovo, in turn, has not been able to join UEFA, which only accepts applications from countries which are recognised by the UN. FIFA allows its members to play teams from Kosovo in "youth, amateur, women's and club football" but has stopped short of permitting full internationals.