A key player in Russia's midfield, Shirokov picked up a knee problem at the end of April and was subsequently left out of Fabio Capello's squad for the trip to Brazil.
Capello labelled Shirokov as a "very important member" of the squad, but with the Zenit St Petersburg star set for surgery in Finland, recovery in time for their opener against South Korea on Tuesday in an impossibility.
Mogilevets, who ultimately replaced Shirokov in the squad, has thanked the 32-year-old for giving him guidance earlier in his career before adding that Russia are missing out on a "very strong" midfielder.
"It was noticeable how much he was upset," Mogilevets told the Russian Football Federation website. "But when we were together in Zenit Roman constantly helped me.
"He told me how to play better in this or that situation. He helped me and this helped me a lot in the future.
"I wish him a speedy recovery. He is a very strong player."
Russia coach Capello came in for significant criticism for his man-management skills when in charge of England.
And Mogilevets revealed that he has not had much contact with the Italian before praising the coaching staff of his club, Rubin Kazan.
"Personal conversation never happened," said the 21-year-old. "But the coach is constantly giving to understand each player in the team that counts on him.
"I must thank the coaching staff of Rubin for believing in me and given the chance (to prove himself)."
