Capello quit his job following a meeting with FA chairman David Bernstein and general secretary Alex Horne at Wembley Stadium on Wednesday, where they discussed the decision to remove the England captaincy from John Terry and the manager's response through an Italian broadcast interview.
Fabio Capello: "I leave England and I will not say anything else."
When asked about the quotes attributed to him by other Italian news agencies, he said they were "false".
The FA are red-faced over the situation and have struck a deal to keep everything under wraps.
The Italian press have been left stunned by Capello's resignation as England manager but are already focusing on his next destination.
"Capello shock resignation," ran Gazzetta dello Sport's headline, which added: "The Italian tactician has felt betrayed by the federation. He was the coach since 2007 and leaves England four months before Euro 2012."
Gazzetta says the veteran coach will have no problem finding a new job.
Capello, who has enjoyed successful spells at Juventus, Roma and AC Milan, has been linked with Inter Milan since last summer.
Russian side Anzhi Makhachkala are also reportedly keen to acquire his services.
"Beware of (Inter Milan president Massimo) Moratti and Anzhi," Gazzetta warned.
"There is also the possibility of (Juve president Andrea) Agnelli (offering the manager's role)."