Ireland needed victory at the Stade de France to put one foot in the knockout stages but they will now head to Parc des Princes next weekend needing to secure a bonus-point victory against Argentina.
Vincent Clerc, who broke Irish hearts at Croke Park in February, plundered another two tries in a one-sided second half.
But it was Clerc's Toulouse team-mate Jean-Baptiste Elissalde who laid the foundations by kicking five penalties that edged the hosts into unassailable lead.
O'Sullivan now faces the undeniable task of lifting a squad low in confidence and besieged by off-field problems before the return to Paris.
But the Ireland coach will not raise the white flag before a bitterly disappointing World Cup campaign is finally put out of its misery against the Pumas.
"Playing Argentina is going to be another challenge," he said. "We were hoping France would not play as well if we did not get a lead but they played well.
"I'm not sure exactly what is required to qualify. I used all my energy preparing for this game.
"I believe we have a chance this week if we get the job done. This is the pool of death and we knew it might go down to the last game.
"We have a nine-day turnaround, which is good. We will get a plan ready for Argentina.
"We will dwell on this for 24 hours but we have to move on."
O'Sullivan claimed his side's huge penalty count - freely punished by Elissalde - contributed to the defeat and admitted the simple truth that France were by far the better team.
"We are obviously disappointed to be well beaten, and the better team won," he said.
"The penalty count was eight against Ireland at the end of the first half so that was a problem.
"We were being blown off the park there and it was more of the same in the second half. France built a lead on our indiscipline.
"We also needed a good line-out but that wasn't working either. So a combination of a lack of discipline and a poor line-out put us in a bad place."