"We have submitted seven video-recordings clearly showing Brych's tendency to make decisions against our national team", said a statement from the Serbian association.
However, Shaqiri and Xhaka caused a bit of controversy with their goal celebrations that is believed to similar to the eagle flag of Albania, which could cause political tensions in the Balkans.
Many people in the former Serbian province of Kosovo, which has an ethnic Albanian majority, identify with the red and black flag. Shaqiri was born in Kosovo.
The build-up to the match had seen exchanges between Serbian players and Shaqiri, who wears boots with the Kosovo flag displayed on one heel and the Swiss one on the other.
Xhaka and Shaqiri celebrated their goals by making a nationalist symbol of their ethnic Albanian heritage.
The Polish Football Association was fined 10,000 Swiss francs ($10,100) and given a warning by FIFA's disciplinary committee on Saturday for a banner that the governing body deemed political and offensive.
Kosovo declared independence in 2008, less then a decade after the 1998-1999 war between ethnic Albanian guerillas and Serb forces, but Belgrade - backed by its traditional ally Russian Federation - still refuses to recognise the move. I spoke to the father of one of our players who is Albanian, and he told me about this history.
They said the two players' "political sensibility and social awareness were undeveloped" and that they should have followed the lead of the national coach "who ignored all political undertones" to the match.
Switzerland's last-gasp victory against Serbia in their second World Cup match on Friday night threatens to be overshadowed by the celebrations of its two goal scorers.
The Argentinian FA and Croatian FA have also had disciplinary proceedings opened against them after crowd disturbances.
Meanwhile, the Serbian papers also slammed what they labelled "shameful provocation" by Shaqiri and Xhaka.