The centre-half was forced off after just eight minutes at Turf Moor with a groin injury, with Burnley going on to win 2-0 after second half goals from Josh Cullen and Jaidon Anthony.
Le Bris felt Ballard was a big miss after he was replaced, but says he has no sense at this stage as to how serious the problem might be.
“We especially missed him against direct play like that,” said Sunderland’s head coach.
“When we pressed high, they went long all the time, and Ballard is always really important in that situation.
“We’ll wait until Monday to have a diagnosis.”
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Sunderland had two glorious early chances at Turf Moor, when Eliezer Mayenda was denied by Martin Dubravka and Chemsdine Talbi chipped wide.
Burnley had a Lyle Foster goal disallowed in the first half, but took the lead just two minutes after the restart when Cullen curled into the far corner. Anthony then sealed the win in the final minutes.
Le Bris said: “I’m disappointed, because I think we started well, our first half was positive, we created two chances, and we were in our game plan. I think we dominated this first half.
“But at the beginning of the second one, we made a small mistake and conceded this goal, and after that the game changed completely, they dropped into their back five, deep, well-organised, aggressive block, and we struggled to find the good tempo, the good rhythm, to create chances.
“In that situation, when you are a bit sloppy, but not accurate enough, I think it’s really obvious that you will concede counter-attacks, and that was the story of the second goal.”
The missed early chances proved costly for Sunderland.
Le Bris said: “We’ve talked a lot in the build-up to the season about being clinical, and how important that’s going to be. The first goal was very, very, very important.
“Fine margins, and if you score early, because it was possible today, I think the scenario changed completely, and for us it would have been the best option.
“We created this chance, so it’s positive, I think, because sometimes you don’t create anything.”
Despite their first half chances, Sunderland struggled to create any opportunities after Burnley’s opening goal, but Le Bris insists that isn’t a concern.
“Not at the minute, because we know that this problem is really hard to solve,” he said.
“It’s not just about us, it’s about every team in the league when you face a well-organised block like that, you need probably better references, shared references, better culture, and we’re still in construction and work in progress for our team.
“We started with eight or nine new players, so this situation is probably the most complicated, so I’m not too worried. I just know that we have to improve this part.”
