And having won just one of their opening five Ligue 1 fixtures, Mavuba is demanding better.
"We have a big game on Sunday against Lyon," he told France Football.
"We have to bounce back and try to beat Lyon, who are a tough opponent.
"We (the players) are all in the same boat, it's everyone's business.
"We have to respond collectively as it is in difficult times that you see how the squad behave."
The defeat to BATE was a heavy blow to Lille's hopes of advancing from a group which also includes Bayern Munich and Valencia.
Mavuba added: "We lacked aggression and commitment, which is amazing as we fought so hard to get in the Champions League.
"We reacted after half-time but, at this level, it was too late.
"This is the worst start. You play at home against the team that is supposed to be the weakest in the group and lose 3-1..."