The Black Cats looked to be on the way to a defeat that would have left them in serious relegation trouble when Craig Gardner was sent off for a reckless challenge in the 34th minute. They had already slipped behind to a 10th-minute Jonathan Walters strike and left themselves a mountain to climb.
A second-half display full of drive and commitment yielded a point courtesy of John O'Shea's 64th-minute leveller.
"In some way we are a masochistic team," said Di Canio. "It is a massive point for us but it wasn't easy. After 10 minutes we gave an easy goal away even if we knew before kick-off that they had five or six who are giants compared to our physical presence."
He added: "The first corner kick we conceded we give a goal away. Then you saw Craig's bad challenge. We have to be careful and to handle our aggression. We have to make sure we don't repeat the same mistakes otherwise we are in real trouble."
There was no disputing the legitimacy of Gardner's red card, with his studs-up challenge on Charlie Adam coming right in front of referee Lee Mason.
Di Canio refused to be overly critical of his player but revealed he had no time to talk to him in the aftermath.
He added: "I love Craig because he has heart, passion, dedication. He is an amazing professional but now we have to be careful because there are two games to go and we do not have the time to recover from these mistakes.
"As I told you with Sessegnon, I don't want to speak about him because he is out.
"At half-time Craig was out and he can't play anymore. What am I going to tell him? There will be a moment but I had to be focused on my players and the players on the bench to see if I could change something.
"He was down, very sad and at the end of the game he said sorry. I'd like to see my players walk inside the dressing and not have to say sorry. It's another mistake and it can happen but we need to improve this."