The Italian - who spent around six months in charge at the Stadium of Light in 2013 - was reacting after Sunderland fell to a humiliating 4-0 defeat to Aston Villa on Saturday, leaving them just above the bottom three.
"I don't know what's happening now, but it looks like the team is drifting," Di Canio told Fox Sports.
"It's not Poyet's fault, because chairman Ellis Short is the real origin of all these troubles. I saved Sunderland when the club was sinking; along with my staff, I completed a true miracle, on and off the pitch.
"We tried to change the philosophy of the team: in the two previous years, no fines were given, despite of players getting drunk and partying until late, even a few days before a match.
"I was giving fines even for [players being] five minutes late. It's fundamental, to keep order in the dressing room. I took all the responsibilities, but my project was immediately cut off.
"It was a choice which came from above.
"I don't want to blame Poyet, but if you're afraid to fine one of your players, then you have to expect some troubles."
