Sunderland take on Southampton in their final home game of the season on Sunday knowing a victory should pretty much guarantee their top-flight status.
The Italian coach believes his side can get the points that are needed and says the 1-1 draw against Stoke last time out has lifted confidence.
He said: "We are fully confident; the second half especially gave us more belief and an extra lift," Di Canio told the club's website.
"Now we have another massive game because we know that if we win, we stay up."
Despite his upbeat assessment of the relegation scrap, the Black Cats boss has called for an improved positive mentality at the club moving forward.
"Daily I discover other traits and character of this environment, and in general I am not enjoying," he added. "Too much, people spend time watching other [teams], which is normal at this stage of the season.
"But it is a habit in this environment which I want to change completely. We delegate our job to others. That is not my idea, I want to do my own job. I want to think positively in the way we do things, not wait to try for others to do things for us.
"To change the mentality normally takes a few months, but we have to start from now. We have to think only and focus about our game. Our destiny is in our hands."