The Italian was furious last week when he came across staff at the club's Academy of Light training base celebrating Wigan's defeat by Swansea which handed the Black Cats the chance to secure their Barclays Premier League status against Southampton on Sunday.
That looked to be on the cards when full-back Phil Bardsley blasted them into a 68th-minute lead, somewhat against the run of play, but they eventually had to settle for a point after substitute Jason Puncheon levelled within eight minutes to ease the Saints over the finishing line.
Sunderland will be safe without kicking a ball if 18th-placed Wigan lose at Arsenal on Tuesday evening, but even if the Latics were to win a point at Tottenham on the final day would keep them up because only one of the Latics and Aston Villa, who meet at the DW Stadium the same day, could overhaul them.
Di Canio said: "To be honest, the players have done an amazing job because it was difficult. Even if you are a good manager with a good staff who tries to help psychologically during the week, when you work with some habits for eight months, it's difficult.
"Even if you try to believe in something more, it's difficult. But I have to tell you, they have done a fantastic job in my opinion."
He added: "If we get one point, we are mathematically safe, so it's good to arrive at the last game and know if we draw or if we win, we stay up so it is in our hands. That is already a good signal."