The Black Cats boss demanded that his side show more desire after "humiliation" at the hands of Aston Villa, which boosted its own survival hopes with a 6-1 victory.
Di Canio had guided the Black Cats to victories over Newcastle and Everton that had boosted their hopes of Premier League survival but now lie above Villa only on goal difference.
The Italian boss believes one more win will secure the club's safety but demanded that his players come back down to earth quickly.
"It's a very bad defeat and our performance I'm not very happy about, obviously, but probably we thought the main job [of survival] was done," Di Canio told Sky Sports. "If the team has performed in this way, the first person responsible is the manager, and also the players, but the signals we probably didn't read in the week. Maybe this is a medicine in some way that can let us understand that we have to play with desire, commitment, otherwise we are going to have difficulty. This humiliation can help the players, the manager, the staff.
"We need a minimum of another three points. We can do it, but it was unacceptable the performance we made tonight. There was one team that played like it was the last chance of their life, which was Villa, and a team that was probably a little full in the stomach because of the last two wins in a row."
Sunderland was dealt another blow in the second half when Stephane Sessegnon was sent off for a challenge on Yacouba Sylla. The three-match suspension for a straight red card would rule the forward out for the rest of the season but Di Canio confirmed he would appeal the dismissal.
"We saw the clip and there is not a bad challenge," the former West Ham striker added. "In my opinion it wasn't a red card. I think once the referee has seen the clip he's going to realize the dynamic of the challenge can put him in difficulty.
"In reality, when you see the clip there isn't any intention to damage the opponent. The leg was not raised. We're going to appeal, of course."