Vulcano arrived to join the new-look Sunderland coaching team as assistant head coach in the summer but the decision was made for the 37-year-old to move on after just six months at the club.
Sunderland don't plan to replace Vulcano directly, with Le Bris instead revealing there'll be slight tweaks to the day-to-day work of his remaining staff members. And Vulcano, he says, left on good terms.
Vulcano joined in the summer having left Al-Nassr, in Saudi Arabia, where he worked as part of Stefano Pioli's coaching team, overseeing a squad that included Cristiano Ronaldo.
Pioli wanted to take Vulcano with him to Fiorentina - he didn't last very long in that job and was sacked in November - but the opportunity to work in England and the Premier League was a huge appeal.
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Vulcano said he had previously been close to taking a job at Sunderland but felt the timing wasn't right, but was delighted to join in the summer. But his stint at the club was short lived.
"First of all, I appreciated working with him, as a person and as a professional," said Le Bris, explaining Vulcano's exit.
"We decided to stop the collaboration because we didn't find the right fit in our current staff.
"The staff is always evolving, like players. We have young members of staff, some of them can step up, some of them can just stay at the same level, and our structure is really dynamic.
"So for Luciano it wasn't easy to find the right position, and rather than forcing things, we decided together that it was better to stop there.
"Even if we stopped here, he helped the coaching staff, it's really obvious. But after that, you have to feel good in your daily dynamic, and it was the case for both sides.
"I repeat, rather than forcing things, it's better to stop and wish him the best. I think he's a good professional, so he will succeed as well."
Le Bris continues to be supported by assistant head coach Isidre Ramón Madir, who also arrived in the summer as well as Michael Proctor and Alessandro Barcherini.
Neil Cutler also arrived as the club's new goalkeeper coach in the summer, while James Brayne was appointed to lead the first team's set-piece coaching.
Sunderland head to Arsenal on Saturday looking to build on their impressive win over Burnley on Monday night, but the Black Cats will again be without injured skipper Granit Xhaka.
There was better news on the injury front, however, with Le Bris confirming Omar Alderete is fine and available after the defender limped off against the Clarets.
Deadline day signing Nilson Angulo could also be available, despite only being scheduled to arrive on Wearside on Thursday evening.
Xhaka has missed Sunderland's last two games after suffering an ankle injury in the win over Crystal Palace. The plan is to closely assess the injury next week, with Le Bris previously suggesting the captain will likely miss next week's visit of Liverpool and the FA Cup trip to Oxford.
Le Bris said: "No update on Granit yet, but he's doing well. He was running on the treadmill today, so it's positive.
"Nilson will arrive this evening. We'll see when he'll be with us. He played a lot, so he's fit.
Now it's a question of connection with his teammates, with the squad. It could be quick and I hope it will be the case. We'll see, but he could be involved on Saturday."