The Black Cats' new boss tasted defeat in his first game in charge on Sunday, with a 2-1 setback suffered at top-four hopefuls Chelsea.
Defensive mishaps cost Sunderland dear at Stamford Bridge, but there were positives to be taken from a game which saw their winless run stretched to nine.
Di Canio is determined to ensure that no mistake is made twice, with only goal difference keeping his side out of the bottom three, and is looking for his players to prove that they have what it takes to preserve their top-flight status.
He said: "We've got to do much better. The lads are ready to work hard and we'll analyse the mistakes.
"That way people can improve and next time they'll consider doing something else."
Next up for Sunderland is a Tyne-Wear derby against local rivals Newcastle United, and the selection dilemmas are stacking up for Di Canio - with the suspended Craig Gardner joining injured duo Steven Fletcher and Lee Cattermole on the sidelines.
Di Canio added: "It's obvious that Craig is a key player for us. He's one of the fighters on the field. He's one of the leaders of the team.
"But we don't have time to cry. We've lost Danny Graham too, but we have enough players to get results."