Tries from Fergus McFadden, Tomas O’Leary and Jamie Heaslip were not enough to prevent the champions from leaving Dublin with a second win of the tournament.
And O’Driscoll viewed the afternoon as a missed opportunity after Ireland were once again undermined by errors.
“We had a chance with three minutes to go. We were 10 yards from their line, they were scrambling but we coughed up another ball,” said the captain. “I thought we were going to do to them what they did to us at Croke Park four years ago when they won in the last minute, but again we coughed up the ball too easily.
“When we scored our tries we had taken it through a number of phases, but when you turn it over after three or four it’s hard to build momentum.
“The chance was there for us to take it but we didn’t. That’s a bitter enough pill to swallow.
“We felt like we had massive capability to score tries. The chances were there but we weren’t clinical and that’s what’s killing us.
“There are just little things that need tweaking, but these are the fine lines between winning and losing Test matches.”
Ireland staged a late do-or-die assault but France responded with some desperate defence.
France coach Marc Lievremont, said: “We’re very satisfied with the outcome. In the last few minutes there were mistakes due to impatience and this made the match stressful.”