Totti hit back by stating the much-travelled Di Canio was "an expert on flags (symbols of a club), having waved so many in his career."
Yesterday afternoon the ex-West Ham United man continued the verbal sparring through the media.
"Whoever wrote Totti's script could've done better," replied Di Canio, who is now a television pundit.
"The thing about the flags is a joke the Romanisti have been using for 10 years. It's true I must justify my cachet, but I do so by saying what I think.
"I repeat that in my view Totti did not behave like a leader against Inter. You can be a champion and you can be a 'flag,' but still not be a leader."