Russia bowed out of the Brazil showpiece on Thursday after Algeria came from behind to salvage a 1-1 draw against them in Curitiba.
Former England boss Capello was left seething at the officials after lasers were shone at goalkeeper Igor Akinfeev throughout the match, in which Islam Slimani cancelled out Aleksandr Kokorin's early strike.
Needing a win to stay in the tournament, Russia will now leave Brazil, but Capello – who extended his contract until 2018 earlier this year – defended his record and wants to stay on.
"I will continue to work for the Russian national team, if they want me to continue," Capello said.
"I have done a good job. England went to the (World Cup) knockout round in 2010 after failing to qualify for Euro 2008.
"Russia qualified for the World Cup for the first time in 12 years."
Capello – highly successful in Italian club football – has now won just one of his seven World Cup matches as a coach.
He led England to the 2010 World Cup, but they won just once before a 4-1 thrashing at the hands of Germany ended their campaign in the last 16.
And two draws and a defeat were not enough for Russia to progress through the group stages of this year's tournament.
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