The tries from debutant lock Pascal Pape and centre Yannick Jauzion came just after the Irish had stunned the French by scoring a try themselves through Anthony Foley to pull to within one point of the hosts at 11-10.
"The killer was the two tries in a four-minute period," said 45-year-old O'Sullivan, who was missing six first-choice players which, added to the retirement of world class hooker and captain Keith Wood, left Ireland's resources seriously stretched.
"We contributed to those tries more than they (the French) did," he said.
"Mistakes come from pressure and at this level against teams with that pace and power you get punished cruelly."
O'Sullivan praised his side for sticking to its guns and even responding with a try of its own through winger Tyrone Howe.
"Those tries could have kicked the guts out of us.
"But we kept battling away and kept our composure and scored another try."
However the always honest Irish coach said he had no arguments with the result.
"Four tries to two is a reasonable reflection of the game but 3-2 would have been fairer," said O'Sullivan.
He was however a happier man than the one who admitted to feeling sick to his stomach after the 43-21 defeat by France in the World Cup quarter-finals last November.
"This restored some of our self-respect we lost last time against the French. This was more like us."
In contrast to his French counterpart Bernard Laporte who criticised the kicking of Frederic Michalak, O'Sullivan was delighted with the way his outstanding fly-half Ronan O'Gara had kicked tactically.
The 26-year-old was also instrumental in the two tries scored.
"We started the game pretty well, we were kicking pretty smartly but they took charge in the second-half," he said.
"The better team won on the day - the French had four chances and they stitched us up every time."
O'Sullivan, though, hoped that at least one of the major players he was missing for this match would be back for the clash with Wales next weekend - talismanic centre and captain Brian O'Driscoll.
"We were missing six frontline players including O'Driscoll, who is 95 per cent on his way to being fit for the Wales match," he said.
Paul O'Connell, his temporary replacement as skipper, admitted it had been a hard match, although the 24-year-old had an outstanding match alongside second row partner Malcolm O'Kelly.
"It was really tough and I was just a bit disappointed we didn't get the scores we felt our pressure deserved," he said.
Ireland take on Wales in their second game of the 2004 RBS Six Nations Championship at Lansdowne Road this Sunday (22nd) at 3pm.