The Black Cats are now only out of the bottom three on goal difference following the weekend results and have the small matter of the Tyne-Wear derby against Newcastle as the first of their final six games.
Cesar Azpilicueta's own goal shortly before the interval gave Sunderland hope of a shock Stamford Bridge success, but they left West London empty-handed after the unfortunate Matt Kilgallon put through his own net before Branislav Ivanovic deflected home David Luiz's long-range shot.
Di Canio has been impressed with the attitude in the squad despite their perilous position and has backed the Stadium of Light side to pick up points when they tackle opposition less testing than the European champions.
He told Sky Sports: "At the moment everything is negative, but we are not worried because we are going to do the right job to stay in the league.
"I believe in the quality of my players. When I decided to come to Sunderland I knew which players were here. Despite the environment and the situation I found a very good group of players.
"Obviously we have to work more. They did very well in the last few days and now we will see if they can give me the same ability for the next six games.
"The first half gave me a very, very good feeling for the future because we are not going to play against Chelsea every time, they are one of the top four sides.
"It is obvious that the job has to come from us because maybe we will play against a weaker side than Chelsea."