Iliman Ndiaye struck Everton's opener before Grant Xhaka found an equaliser for Sunderland in the opening minutes of the second-half.
Speaking post-match, Le Bris said: “It is a good point in the end. We didn’t start well, and they were better than us for the first 30–35 minutes.
“They are a good side with many threats. They have the ability to exploit our turnovers, and we were not consistent enough in the first part of the game to be competitive.
“We switched on in the last part of the first half, and the second half was much better - we probably deserved to score a second goal.
“It was really important to score the goal at the start of the second 45. It gave us momentum - Granit drove us on in important moments, showed quality to get his goal, and was important for us once again.
“We will face different scenarios this season. Sometimes you don’t know why, but you can switch it. We are still connected with our ideas, and that was how we got back into this game.
“With our fans, when we can generate positive actions, we feel their intensity. It wasn’t enough for the second goal, but I hope it will be the case next time.”