Capello named five strikers in his provisional 30-man party, but only three - Aleksandr Kerzhakov, Aleksandr Kokorin and Maxim Kanunnikov - made the final cut, while Artem Dzyuba made the Italian coach's list of five reserves.
Pogrebnyak, who scored 13 goals in 39 league games for Championship club Reading this season, was the only forward to be culled and the 30-year-old could not hide his disappointment.
"I am a bit shocked and didn't believe that I had been excluded from the squad," Pogrebnyak told 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."
Kokorin scored the most league goals this season of the strikers in the final squad, as he hit the back of the net 10 times for Dinamo Moscow, while Kerzhakov struck six for Zenit and Kanunnikov (Amkar Perm) notched three times.
Dzyuba was the leading Russian scorer in the Russian Premier League with 17 goals for Rostov.
Capello named his provisional squad on Monday, with Pogrebnyak a surprise selection as the forward had never played during the Italian's tenure as Russia's coach.
The squad had yet to come together before the final 23-man group was named and Pogrebnyak was bemused why he never got a chance to prove himself to Capello.
The deadline for final squads is June 2.
"It's a shame that I was not given any practice or play - that's too bad," the former Fulham striker said.
"But basically, it's the coach's decision, he is entitled to take the decisions that he sees fit."
Pogrebnyak added: "It is upsetting.
"The World Cup is a dream for any footballer. There are more important things in life but I really wanted to play there."
Aleksandr Anyukov, Aleksei Berezutski, Vladimir Bystrov and Yuri Gazinskiy joined Dzyuba on the reserve list, while Dinamo midfielder Alexei Ionov joined Pogrebnyak in being cut.
Real Madrid winger Denis Cheryshev, who spent this season on loan at Sevilla, will join the squad for experience, but will not travel to Brazil.
Final squad in full:
Goalkeepers: Igor Akinfeev (CSKA Moscow), Yuri Lodygin (Zenit), Sergei Ryzhikov (Rubin Kazan)
Defenders: Vasili Berezutski (CSKA Moscow), Vladimir Granat (Dynamo Moscow), Sergei Ignashevich (CSKA Moscow), Dmitri Kombarov (Spartak Moscow), Alexei Kozlov (Dynamo Moscow), Georgi Schennikov (CSKA Moscow), Andrei Semenov (Terek Grozny), Andrey Yeshchenko (Anzhi Makhachkala)
Midfielders: Igor Denisov (Dynamo Moscow), Alan Dzagoev (CSKA Moscow), Viktor Fayzulin (Zenit), Denis Glushakov (Spartak Moscow), Pavel Mogilevets (Rubin Kazan) , Aleksandr Samedov (Lokomotiv Moscow), Oleg Shatov (Zenit), Roman Shirokov (Krasnodar), Yuri Zhirkov (Dynamo Moscow)
Forwards: Maxim Kanunnikov (Amkar Perm), Aleksandr Kerzhakov (Zenit), Aleksandr 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).
