Aulas made the accusations following Lyon's 2-1 victory at their local rivals on Sunday, when winger Jimmy Briand headed home in the third minute of injury time after Saint-Etienne's Romain Hamouma had cancelled out Alexandre Lacazette's opener.
Clashes between supporters in last season's Rhone derby led to local authorities banning Lyon fans from the Stade Geoffroy-Guichard for the fixture.
But the talking point on this occasion came from the players, with Aulas stating he was struck on the back by France international Ruffier during unsavoury scenes at the final whistle, while also accusing Saint-Etienne goalkeeper coach Fabrice Grange of striking a Lyon team doctor.
Saint-Etienne have refuted those claims and claimed Lyon goalkeeper coach Joel Bats incited trouble by hanging a scarf in front of the south stand.
A statement on the club's official website read: "Neither Stephane Ruffier or Fabrice Grange have shown violent behaviour after the derby in the tunnel leading to the locker room, while Emmanuel Orhant, doctor of Olympique Lyonnais, showed a shameful attitude with provocative singing.
"(We feel) it is Joel Bats, goalkeeping coach of Olympique Lyonnais, who has behaved irresponsibly by hanging a scarf in front of the South Kop without having sought the permission of the Football League as required by regulations.
"This act is a form of incitement to violence and could have serious consequences on the course of the match. If the goal was to provoke an invasion of the pitch to the future harm of Saint-Etienne, the act is even more deplorable.
"Jean-Michel Aulas complained about the travel bans of supporters decided by the state. Is the attitude of Joel Bats and Olympique Lyonnais leaders likely to encourage the government to allow future travelling supporters?"
Lyon's victory on Sunday saw Remi Garde's charges move to seventh in the Ligue 1 table, leapfrogging Saint-Etienne in the process as they slipped to ninth.
