Di Canio was in a reflective mood after the draw at St Mary's Stadium, but was happy overall with a point earned.
"When you get close to the final whistle you hope you can get out with three points. Talking in an honest way we didn't deserve the win.
"Southampton were better than us today, but one point is good enough away from home."
Sunderland were defeated in the last minute against West Brom on the opening weekend through a Rickie Lambert penalty, and Di Canio bemoaned his side's penchant for giving away cheap set-pieces.
"Now we work so hard in trying not to give cheap free-kicks away. If you give 10, 12 set-pieces away it's dangerous, and today the free-kick came from nothing.
"That is something that I don't like."
The Italian appeared to make a last-ditch transfer plea too, bemoaning a lack of physicality in his side.
"When I asked 45 days ago for another central midfielder with a physical presence, preferably British, there was a reason."