A stoppage-time goal by substitute Chemsdine Talbi capped a disciplined performance by Sunderland, who climbed to second in the table.
Sunderland fans streamed out of Stamford Bridge chanting "We're going to win the league", but Le Bris said his priority remained avoiding relegation after the club were promoted from the second tier last season.
"Our target remains exactly the same – we want to reach as soon as possible the target of 40 points," the Frenchman said. "It's important to start well because it creates belief and confidence."
Sunderland's 17 points from their opening nine Premier League games represents the best start by a promoted club since Hull City in the 2008-09 campaign, according to data company Opta.
Le Bris praised his young side for the way they have stuck to his plans back in the top flight.
"What we can control is our way of playing, the energy we can put on the pitch, the togetherness," he said.
Sunderland had to cope with Chelsea taking a fourth-minute lead through Argentine forward Alejandro Garnacho.
Wilson Isidor equalised in the 22nd minute, and in the third minute of added time, Talbi claimed the winner, his first goal for Sunderland since signing from Club Brugge in July.
"We still have a very young squad with a limited shared experience so we have to learn from different situations," Le Bris said. "This one was positive in the end but we were just on the edge in the first minutes."
Chelsea coach Enzo Maresca was blunt about the performance of his side who barely threatened to get a second goal after their early advantage.
"I think in general we were not good enough," the Italian said. "When you are not good enough in the Premier League we know that the consequences can be bad ones."
He said Chelsea paid the price for allowing Sunderland's Brian Brobbey to hold the ball up, with his back to goal, before rolling a pass to Talbi to score with a low curling shot.
"In that case, for sure, we have to do better," Maresca said.