Former Italian international Christian Panucci said Capello had acted in a "shameful way" by not defending him.
Panucci and physical trainer Massimo Neri left their posts with the Russian squad when they were not paid. The Russian Football Federation said this month that Capello, who is reported to have a €7 million annual salary, has not been paid for five months.
Capello "acted in a shameful way with me and with all the Italian staff," Panucci told Gazzeta dello Sport on Tuesday.
"I will tell him face-to-face the next time I see him," Panucci added. "A great coach should defend his staff and he did not do it."
Panucci thanked Capello for the chance to work with the Russian team, who crashed out of this year's World Cup in the first round.
Panucci said the Russian federation had failed to keep promises to renew his contract. "I was working without a contract and then I said to myself 'that's enough!'"
The federation said this month that it could no longer afford the salary of Capello, who has been national coach of the 2018 World Cup hosts since 2012.
Capello last week refused to comment on speculation about his future with Russia.