Les Dogues have won just one game in Ligue 1 this season, while also being humbled 3-1 at home to BATE Borisov in the Champions League.
Roux believes that the performance in Sunday's 1-1 draw with second-placed Lyon has done a lot to instill confidence in the dressing room.
"The senior players aren't worried," Ligue1.com quotes Roux as saying. "I'm not seeing the lads mouthing off and looking discouraged.
"On the contrary, I'm seeing guys who want things to change, who want to start winning. That's what we're working for. When the senior players are like this, the other younger or less experienced players, like me, follow their example. That's how you get out of a situation like ours.
"In terms of points, we haven't been left behind even though there is a bit if a gap. It would be great to follow the Lyon match up with a win and start a solid run. That's what we've been missing."
Lille lie 13th in Ligue 1 with seven points from six games.