The supporters have launched a web campaign and written a letter to FIFA to complain about the referee Terje Hauge and the conduct of the home crowd during Wednesday night's 1-0 defeat in Maribor.
The result put Slovenia through to next summer's finals on away goals , with the aggregate score tied at 2-2, and leaves Russia boss Guus Hiddink considering his future.
Heated: Slovenia keeper Samir Handanovic (second left) clashes with Russia's Aleksandr Anyukov (second right) and Everton's Diniyar Bilyaletdinov (far right)
It is alleged that a small knife was thrown from the crowd towards Russia goalkeeper Igor Akinfeev. And the Russians feel the referee favoured their rivals, paritcularly with the controversial sending off of Alexander Kerzhakov in the 66th minute.
Off day: Yuri Zhirkov is shown the red card by referee Terje Hauge
The striker was dismissed for violent conduct when appearing to make a legitimate attempt to win a loose ball from goalkeeper Samir Handanovic.
Handanovic lashed out and was booked for striking Kerzhakov in the thigh while defender Bostjan Cesar was unpunished for pushing his hand into the face of the Dynamo Moscow player.
Chelsea defender Yuri Zhirkov was sent off for a second bookable offence in injury time for pushing an unused Slovenia substitute while trying to retrieve the ball for a throw-in.
The open letter reads: 'I beseech you, Russia needs a replay of the match with Slovenia and requests the dismissal of referee Terje Hauge.
'We must do something. We fight for fairness. Furthermore, during the second half, someone throw a knife, which fell near the goalkeeper, Akinfeev. Terje Hauge saw this incident but did nothing to stop it.'
The referee was seen handing an object to his fourth official during the second half, but it is unclear what it was or if the incident has been reported.
Russia have history with Hauge. The Norwegian sent off Andrey Arshavin in Russia's final Euro 2008 qualifier against Andorra two years ago. Hiddink's team secured a nail-biting 1-0 win to take them to the tournament, but Arshavin was banned for the first two matches.
Battle: Handanovic (left) and Bostjan Cesar lash out at floored Russia striker Alexander Kerzhakov, who was sent off for a perceived foul on the goalkeeper
Meanwhile, Hiddink has returned to Holland following the failure to qualify for South Africa 2010.
Decision time: Guus Hiddink must decide whether to stay on as Russia boss
TheRussia Football Union have offered him a new two-year contract, but theformer Chelsea interim manager says he is no rush to sign it.
The63-year-old has the overwhelming support of Russia players to continuein the post, though there have been some dissenters who blame his poorcommand of the language as a reason for him to leave.
Hiddink has other offers, though his decision could rest on who is named the next president of the RFU.
Vitaly Mutko is being forced to stand down from the post next week and Hiddink supports Roman Abramovich's right-hand man Sergei Kapkov to be put in place.
Kapkov is currently head of the Abramovich-sponsored National Academy Fund, which effectively pays Hiddink's wages.
After the defeat by Slovenia, Hiddink said: 'I have an existing contract until the end of the World Cup finals in July 2010.
'The question (of whether I will continue to Euro 2012) will require some time for thought.
'Before the matches with Germany and Slovenia the Russian Football Union expressed their desire to continue working together. But we'll talk about the future at a later stage.'
Regarding plans to install Kapkov as RFU president, Hiddink said earlier: 'I would support him. It would make my job as Russia coach much easier.'
Ex-Chelsea boss Hiddink considers future after Russia's nightmare defeatSlovenia 1 Russia 0: Dedic decider sends hosts into World Cup dreamlandHiddink hails Premier League for toughening up Everton's BilyaletdinovYou must be joking! Everton star Bily finds banter is part of English footballZhirkov risks injury for Russia and blames pain on London climate Explore more:People:Andrey Arshavin, Roman Abramovich, Yuri Zhirkov, Thierry HenryPlaces:South Africa, Slovenia, Republic of Ireland, Andorra, Russia, The Netherlands, GermanyOrganisations:Dynamo Moscow