Pogrebnyak, 30, who has yet to appear for his country under Capello, had been a surprise inclusion on Monday.
“I am a bit shocked and didn’t believe that I had been excluded from the squad,” Pogrebnyak, whose last appearance for Russia came against Greece in June 2012, said in an interview with Sovetsky Sport.
“I hoped that I would be part of the squad, I kept myself fit and was grateful for the faith that was showed in me.
“However in just a couple of days they took away that hope from me.”
The former Fulham forward scored 13 goals in 39 Championship appearances for Reading in England’s second tier this season.
“Of course it is upsetting,” he added.
“The World Cup is a dream for any footballer. There are more important things in life, but I really wanted to play there. The head coach has the right to pick the squad he wishes.”
Artem Dzyuba, the second leading scorer in the Russian Premier League this season with 17 goals for Rostov, was put on a reserve list along with defenders Alexander Anyukov and Alexey Berezutskiy and midfielders Vladimir Bystrov and Yury Gazinskiy.
The Russian Football Union said that forward Denis Cheryshev would join the squad to gain experience but would not travel to the Brazil finals where Russia have been drawn in Group H along with South Korea, Belgium and Algeria.
Squad Goalkeepers: Igor Akinfeev (CSKA Moscow), Yury Lodygin (Zenit St. Petersburg), Sergey Ryzhikov (Rubin Kazan).
Defenders: Vasili Berezutskiy (CSKA Moscow), Vladimir Granat (Dynamo Moscow), Andrey Eshchenko (Anzhi Makhachkala), Sergey Ignashevich (CSKA Moscow), Alexey Kozlov (Dynamo Moscow), Dmitry Kombarov (Spartak Moscow), Andrey Semenov (Terek Grozny), Georgi Schennikov (CSKA Moscow).
Midfielders: Denis Glushakov (Spartak Moscow), Igor Denisov (Dynamo Moscow), Alan Dzagoev (CSKA Moscow), Yury Zhirkov (Dynamo Moscow), Alexey Ionov (Dynamo Moscow), Pavel Mogilevets (Rubin Kazan), Alexander Samedov (Lokomotiv Moscow), Victor Faizulin (Zenit St. Petersburg), Oleg Shatov (Zenit St. Petersburg), Roman Shirokov (Krasnodar).
Forwards: Maxim Kanunnikov (Amkar Perm), Alexander Kerzhakov (Zenit St. Petersburg), Alexander Kokorin (Dynamo Moscow)
Reserve list Defenders: Alexander Anyukov (Zenit St. Petersburg), Alexey Berezutskiy (CSKA Moscow). Midfielders: Vladimir Bystrov (Anzhi Makhachkala), Yury Gazinskiy (Krasnodar). Forward: Artem Dzyuba (Rostov).
(Reporting by Dmitriy Rogovitskiy; editing by Justin Palmer)