Borini came on as a late substitute for the outstanding Luis Suarez but went off in agony with a suspected dislocated shoulder.
Liverpool had used all their substitutes and so finished with ten men as they emphatically ended a five-match winless run in all competitions.
Rodgers told Sky Sports: "I think he'll be out for the season.
"It's unfortunate for Fabio because he has done his other shoulder before and had a similar thing so it looks like the early stages of that again, but the other shoulder which is a big disappointment.
"He came on for 15 minutes and looked quite bright in his movement and he worked very hard to try and stop the forward pass and obviously got injured."
Though Swansea were under-strength due to having one eye on next weekend's Capital One Cup final, Rodgers was pleased Liverpool took advantage and also kept a clean sheet.
"It was an important three points," said Rodgers. "We've had a bumpy road in terms of games Monday and Thursday but the Premier League is very important for us and we knew we had to show focus and determination.
"I don't think you can take anything away from the Liverpool players but it (the final) was something Swansea were thinking about.
"It was a brilliant performance and it's a big applause to the players because their attitude was fantastic throughout the game.
"It was important for us today for a clean sheet, believe it or not even though we scored five goals and I think we had 35 shots.
"It was our main focus going into the game was about being defensively solid and compact against obviously a Swansea team and players that I know very well.
"So all round a fantastic performance and a good three points for us."