The match at the Stade Velodrom seemed destined to end a goalless draw until a injury-time goal from Aaron Ramsey gave Arsenal all three points.
The result propelled Arsene Wenger's side to the top of Group F ahead of their opponents.
"I'm still feeling the shock of the defeat. The scenario is very bad. We weren't great but we weren't terrible either," said the defender.
"We paid the price for letting our attention slip once.
"We are truly shattered [by the loss]. We'll have to show that we are men and go looking for three points against Ajaccio.
The two sides will meet again for the follow-up match at the Emirates on Tuesday, November 1.