Swiss youth international Pajtim Kasami took advantage of the visitors' only clear-cut chance to head home the winning goal five minutes into the second half and get his side off to a flying start.
Di Canio was clearly frustrated by his side's inability to make the most of their chances with new boys Cabral and Ondrej Celustka among those who came close in a dominant opening period.
Di Canio said: "We weren't really ferocious. We have to be nasty in terms of our football.
"I don't want to say we had a clear identity but a big part of the puzzle is clear. I think we did well but it's obvious we can do much better."
Key to Di Canio's plan to move forward is the acquisition of at least two more new players and the Italian reiterated his desire to bring in an influential midfielder before the transfer window shuts next month.
Di Canio added: "Today we had the quality of Cabral but we need another player there who can feed my striker and my wingers.
"We can improve this area if we bring in another player with the key - a real playmaker with a personality and a physical presence because this is the art of the game.
"I told them before the start of the season if we play well and deliver a clear identity on the field I prefer to lose and play well rather than win and play very bad - but after that I think a few points will be better.
"The only disappointment is when you dominate and create 10 clear chances and they had only one corner kick. There was only one team in it, but you have to work on it and take the positives."
Stekelenburg was substituted midway through the second half after sustaining an apparent shoulder injury saving from Jozy Altidore, and Jol admitted the Dutchman could now face a spell on the sidelines.
Jol said of Stekelenburg's injury: "Hopefully it's not as bad as it looks now. It's painful and it could take more than a couple of weeks."
Richardson sustained a hamstring injury after just 19 minutes and Jol added: "Kieran had a great pre-season so it is not the perfect scenario, but it is almost perfect to have the three points.
"When you play against Sunderland you have to get out from the back and I was disappointed with the way we wanted to win the game - in hindsight I was very pleased with the result but we have to do better in future."
Jol expressed delight with Kasami's first Fulham goal, which came after the player spent the latter half of last season on loan at Swiss club Luzern.
Jol added: "For a young kid to score his first goal and the winning goal in the Premier League is of course what I want from him.
"I want him to be happy and enjoy his football and develop himself. I sent him to Switzerland last year because he's a good talent and a strong kid. I thought it was a good chance to start Kasami and I'm glad I chose him."