"Honestly, I deleted all the apps [from my smartphone], I don't read anything, but I hope that the fans have a good opinion of the [Russian] team and the World Cup on the whole," Granat told journalists.
He added that the team had watched their opponents' last matches and were training hard for the tournament.
"I think we'll go into the matches in an optimal condition," the 31-year-old Rubin Kazan player said.
Granat also named Colombia as one of the favorites to win the World Cup.
"The team's lineup is strong," he said.
The host nation will face Saudi Arabia at Moscow's 81,000-seat Luzhniki Stadium on Thursday, before taking on Egypt and Uruguay in their other two Group A matches.