The Black Cats head for West Brom on Saturday stuck at the bottom of the table with just a single point from their four games to date.
Di Canio insists he is not concerned by a run of results which could get worse before it gets better with leaders Liverpool due at the Stadium of Light next weekend and champions Manchester United following hot on their heels.
However, the 45-year-old Italian knows how much of a boost a win over the Baggies, who are only a point better off, could provide and he is challenging his players to make a statement.
Di Canio said: "Paolo Di Canio is the first responsible because I pick my players, I choose the strategy of how we have to play. I absolutely always agree with this: the manager is the number one responsible.
"But the players have to feel a responsibility. They are adult footballers who have to have the desire and the courage to say, 'Yes, we lost, we lost, but I am sure I did my best'.
"It doesn't mean you can be bad or not give quality in training sessions, you have to be professional. Don't smile, but train harder.
"It doesn't have to come only from the manager, otherwise it's tough. This is why I hope we are going to win soon."
Despite Di Canio's insistence that his masterplan will not have unfolded fully until his new-look squad has around 20 games under its belt, he is acutely aware of the psychological effects of a lengthy run of games without a victory.
Sunderland do have a win to their name this season, a 4-2 Capital One Cup second round success against League One MK Dons, although even that was achieved only by way of a remarkable late fightback which saw them score four times inside the final 12 minutes to overturn a 2-0 deficit.
However, the longer their barren league run continues, the more difficult the process of gelling a new squad together - Di Canio made 14 signings during the summer transfer window - will become.
The former Lazio, Juventus and AC Milan striker has learned from experience that players not currently in the team can become restless and upset the harmony within the dressing room as they attempt to stake their own claims.
Asked if he had seen signs of that creeping in at the Academy of Light, Di Canio said: "No, but I know that can happen.
"I can see only someone who is sad because he is not playing and we are losing games. That's typical, you can't be happy.
"I am not worried about a typical situation because I was angry [as a player] to stay on the bench, warming up for 45 minutes and didn't get on the pitch.
"I was upset, but I gave my hand to my team-mates, and then went into the shower and said many bad words inside myself to the manager. But the day after...
"That was my nature, that's why all the managers loved me in my past, because inside I said bad things, but the day after, I was an example.
"But it's difficult to find these examples, like [Ryan] Giggs or like [Franco] Baresi or like [Paolo] Maldini - they played every game, of course, but for others, it's difficult because it's natural, especially with the new generation, that they think, 'If I am here, I have to play. I am better than this guy'.
"Lose, lose, lose, not play, not play, not play - work harder.
"But I haven't seen any big signal about this. But it can happen, and that can be worse because the team doesn't gel together.
"They don't know each other, they are worried to say even tough things that can help."
Defender John O'Shea returns to the squad, as does former skipper Lee Cattermole, who seemed set to leave the Stadium of Light during the summer, and midfielder Emanuele Giaccherini following his recovery from a hamstring problem.