Stekelenburg was substituted midway through the second half, which saw Pajtim Kasami net the winner, 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."
Former Black Cats man 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.
He 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."