Bilyaletdinov, 27, joined Spartak Moscow in January following a disappointing two-and-a-half-year spell with English Premier League club Everton but has struggled to regain his top form.
"It hit me like a bolt from the blue, a real shocker," Bilyaletdinov said about his omission from the squad.
"I didn't expect this at all, to be honest. I just don't know what to do or what to say at the moment."
Zenit St Petersburg winger Bystrov, who like Bilyaletdinov played at Euro 2008 where Russia surprisingly reached the semi-finals under Advocaat's predecessor Guus Hiddink, was also left out of the squad announced on Friday.
In another surprise move, Dutchman Advocaat recalled Sporting midfielder Marat Izmailov, who had not played for the national team since 2006.
Izmailov, once regarded as one of the most talented Russian players and a veteran of the 2002 World Cup and Euro 2004, has struggled to overcome numerous injuries in recent years.
But the 29-year-old winger has shown glimpses of his old brilliance this season while playing for his Portuguese club.
Rubin Kazan defender Roman Sharonov was shocked to see his name on the preliminary list.
"At first, I had thought it was April Fools Day," the 36-year-old, who last played for Russia in 2004, told local media.
Advocaat, who will step down as Russia boss following the Euros to take charge of Dutch club PSV Eindhoven, also called up two newcomers, Lokomotiv Moscow midfielder Magomed Ozdoyev and Dynamo Moscow defender Vladimir Granat.
Euro 2012, co-hosted by Poland and Ukraine, starts on June 8 with Russia playing in Group A along with Poland, 2004 European champions Greece and the Czech Republic.
Squad:
Goalkeepers: Igor Akinfeyev (CSKA Moscow), Vyacheslav Malafeyev (Zenit St Petersburg), Anton Shunin (Dynamo Moscow)
Defenders: Alexander Anyukov (Zenit St Petersburg), Alexei Berezutsky (CSKA Moscow), Vasily Berezutsky (CSKA Moscow), Sergei Ignashevich (CSKA Moscow), Roman Sharonov (Rubin Kazan), Roman Shishkin (Lokomotiv Moscow), Vladimir Granat (Dynamo Moscow)
Midfielders: Igor Denisov (Zenit St Petersburg), Roman Shirokov (Zenit St Petersburg), Konstantin Zyryanov (Zenit St Petersburg), Yuri Zhirkov (Anzhi Makhachkala), Alan Dzagoyev (CSKA Moscow), Igor Semshov (Dynamo Moscow), Denis Glushakov (Lokomotiv Moscow), Magomed Ozdoyev (Lokomotiv Moscow), Marat Izmailov (Sporting), Dmitry Kombarov (Spartak Moscow)
Forwards: Andrei Arshavin (Zenit St Petersburg), Alexander Kerzhakov (Zenit St Petersburg), Roman Pavlyuchenko (Lokomotiv Moscow), Artem Dzyuba (Spartak Moscow), Alexander Kokorin (Dynamo Moscow), Pavel Pogrebnyak (Fulham).
