The Italian won over plenty of supporters when he led his team to a 3-0 victory over arch rivals Newcastle United at St James' Park last weekend.
"I don't want to be a hero now," ITV Sport quotes Di Canio as saying. "I don't want to be a hero when we stay up, I don't want to be a hero next year.
"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 of 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."
Sunderland are currently three points away from relegation to the Championship.