Spectacular strikes from Stephane Sessegnon, Adam Johnson and David Vaughan saw the Black Cats to three much-needed points at St James' Park.
Victory on Tyneside was Di Canio's first as Sunderland boss, in his first derby, and he admits he could not have asked for any more from his squad.
He told Sky Sports: "They were warriors. You can't be more proud than this. They did everything, they gave everything, they left all of their energy on the field.
"It was a fair result at 3-0, so I am very happy for them because they really suffered during the game. It was hard because we knew that we had a team in front of us with fantastic ability and quality.
"They worked through the strategy in a perfect way and it was a good result. It was an important result and they deserved it, so I am happy.
"It means that what I thought when I signed, there is quality in this team. There is absolute quality and it is important that we use it in the right way and play together as a team."
Sunderland now sit three points clear of the drop zone, but Di Canio concedes that there is still a lot of hard work to be done if they are to preserve their Premier League status.
He added: "We have to celebrate, but after tonight look to recover our energy.
"We scored three goals, but before we scored the first goal we gave them a chance to score. We have to avoid that. That has to be the philosophy for now until the end of the season and for the future.
"This is only one result. In terms of the result for this area, it is an incredible step. But in terms of the table, it is only a small step to try and get this club out of the relegation zone. We have to be intelligent because the main job is not done."