The nation's Football Federation released a statement on Sunday expressing their frustration that the game was allowed to go ahead despite the poor weather conditions
Clint Dempsey's 16th-minute strike settled a contest which was blighted by heavy snowfall, with ground staff sent on to the pitch to clear the markings with plows and spades, whilst a multi-coloured ball was used to aid visibility.
The treasurer of the Costa Rica Football Federation, Rolando Villalobos, said in a statement released on Sunday that photographic and video documentation had been sent to Fifa to support the appeal, and called for the officials who allowed the match to go ahead to be punished.
"What happened the night of Friday the 22nd ... has no precedents, since it not only went against the sporting spectacle, but also against the physical integrity of the officials and players," the statement read.
Villalobos also highlighted that, under footballing legislation, ground staff should not have been permitted to enter the field of play during the match to clear the pitch, while arguing that "ball movement became impossible given the quantity of snow on the field."
Team coach Jorge Luis Pinto had called for the game to be abandoned, but USA boss Jurgen Klinsmann insisted it was fair to continue to play since both sides faced the same torrid conditions.
The result on Friday leaves Costa Rica at the bottom of the World Cup qualifying table with one point from two matches. USA sit second with three points.