In only his second game in charge, Di Canio led the Black Cats to their first St James' Park win in 13 years, as they beat Newcastle 3-0 on Sunday.
However, the Italian is adamant that such a victory should not afford him such a status.
"I don't want to be a hero now. I don't want to be a hero when we stay up, I don't want to be a hero next year," he said.
"It's easy for the fans to call the players, the manager, heroes if they do the right things and an incredible job.
"Maybe one day if we win something, they can call me hero, but it's not the time now, even if we stay up. It's not the time for a single game.
"I understand what it means - I used to do the same as a Lazio fan. We won the derby, [Bruno] Giordano was a striker who scored an incredible goal and he was my hero.
"I know, but it's not enough for me, not even if we stay up. If we stay up, it would be a fantastic step to build a good future.
"One day, in 10 years' time if I became the best manager in this club's history, they can call me hero, otherwise it's not enough, one game, two games, 10 games, 20 games.
"In 10 years' time, they will decide if I can be called hero, even if I don't like anyway this adjective, 'hero'.
"But when I deliver a special, special thing, maybe they can call me hero."
Di Canio's laudable pragmatism reflects the position in which he inherited Sunderland from predecessor Martin O'Neill.
They remained outside the Premier League relegation zone only on goal difference and had not won in nine games as they headed for St James', and the three points with which they returned, priceless as they were, may count for little if they lose to Everton at the Stadium of Light.
That is something they have done 12 times in their last 16 league meetings. Di Canio said: "I have to be honest, obviously the day after Newcastle, I saw a very good mood. It was fantastic for the players.
"But I was more happy two days later when we started again with a training session together because, to be honest, I saw them really focused and really concentrated on the next match.
"I was worried the day before I met them because I was thinking, 'I don't know them, I haven't known them for many years, so I don't know how they will react'.
"That can be a poison instead of an extra lift, but to be honest, the way they have done things in the last few days has made me very happy because I have seen them really focussed for the next match."