It got worse for the RFS when UEFA opened disciplinary proceedings against it over the behaviour of its fans in the game against co-host
And there could be further sanctions to come, with UEFA confirming it was still investigating allegations Czech Republic defender Theodor Gebre Selassie was subjected to monkey chanting.
Announcing the punishment for incidents in that game, a UEFA statement read: "The UEFA Control and Disciplinary Body has today decided to impose a deduction of six points on the Football Union of Russia (RFS) in the qualifying round of the next UEFA European Football Championship.
"This decision is suspended for a probationary period running from now until the end of the play-offs of the next UEFA European Football Championship (UEFA Euro 2016).
"The Football Union of Russia (RFS) has also been fined 120,000 euros.
"The RFS was facing charges for the improper conduct of its supporters (crowd disturbances), the setting off and throwing of fireworks and the display of illicit banners at last Friday's UEFA Euro 2012 Group A match against the Czech Republic in Wroclaw.
"An appeal can be lodged against this decision within three days of the dispatch of the written decision."
UEFA opened disciplinary proceedings 24 hours after Russia's 4-1 win in Wroclaw.
Violence erupted at the game when a handful of stewards were attacked by large group of fans in a walkway in the 40,000-capacity Municipal Stadium.
Supporters in the stands also set off and threw fireworks, as well as displaying a nationalist 'Russian Empire' flag, something which has been associated with the far right.
An 'illicit banner' at the Poland game has also landed the RFS in hot water, with fans inside the National Stadium in Warsaw displaying a giant 'This is Russia' flag, something that could be deemed to relate to the decades of Moscow control over Poland during the Cold War.
UEFA, which also opened proceedings against the co-host, issued a statement which read: "UEFA has opened disciplinary proceedings against the Polish Football Association (PZPN) for setting off fireworks at last night's UEFA Euro 2012 Group A match against Russia in Warsaw.
"Disciplinary proceedings have also been opened against the Football Union of Russia (RFS) for setting off and throwing fireworks, displaying illicit banners and the invasion of the pitch by a supporter."
UEFA said the incidents would not impact on Russia's suspended six-point deduction and that the new cases would be dealt with on Sunday.
The build-up to the Poland match was also marred by by violence outside the stadium, trouble flaring after a march by thousands of Russia supporters came under attack by masked hooligans.
It led to 184 arrests, while, according to reports, at least 24 people were injured, including 10 police officers.
"UEFA condemns the isolated incidents that occurred
yesterday in Warsaw prior to and after the Poland-Russia match, when
some groups of known troublemakers pelted the police with missiles and
attacked fans irrespective of the team they were supporting. Those
arrested and charged will have to be dealt with by the relevant
authorities," a UEFA statement read.
"UEFA's philosophy is to create a welcoming environment coupled with a low-profile approach to policing. The focus should be on facilitating the enjoyment of the matches by genuine football fans and isolating the tiny percentage of troublemakers. UEFA is in a constant dialogue with the public authorities in order to achieve this aim.
"UEFA is determined that the overwhelmingly peaceful and festive atmosphere that has so far pervaded at UEFA Euro 2012 will be continued right up to and including the final in Kiev on Sunday 1 July."
The sanctions are a huge embarrassment for Russia, which is facing increasing pressure to deal with fan problems, having been named host for the 2018 FIFA World Cup.
The RFS had urged fans to behave after the Czech Republic game but its appeals appeared to fall on deaf ears.
UEFA president Michel Platini said preparations for Euro 2016 were "progressing well" after a meeting of the organising committee in Lille.