Irish Reaction:Not even Pythagoras would be comfortable with devising the mathematical equation that would explain how Ireland could still qualify for the play-off stages. It's an equation that borders on the impossible. In real terms, Ireland's World Cup ended in Paris last night; for the Irish only darkness in the city of light.

Ireland coach Eddie O'Sullivan bore the expression of a man who had dared to hope only for disappointment to intervene again. It's been his lot at this tournament; a sort of Groundhog Day, like a recurring Christmas Eve, tantalised by promise but nothing materialises.

The last place he wanted to be was on the dais in front of the assembled media trying to explain away why his team have singularly failed to live up to expectation. The uncharitable will say he's enjoyed plenty of practice, albeit in discussing singularly unimpressive victories over pool minnows, Namibia and Georgia.

O'Sullivan admitted: "I thought we defended very well and I think they built a lead against our errors and at 15-3 we needed to get the next score, didn't, and unfortunately that really killed off the game.

"I'm not sure what the penalty count was but it allowed France build the lead they needed and give them a cushion. And at 15-3 they got the penalty which really put the game on a knife edge, and once they got the first try, the game was out of reach: that was really the kernel of it.

"The second thing was our lineout didn't really fire, we needed it to fire to get us into the game. Presentation of the ball didn't give us any front foot ball and a combination like that you're kinda doomed."

When asked about the referee, O'Sullivan said: "I don't know, it's hard to say. I don't want to criticise the referee because that will only lead to more trouble. It's not like us to give away so many penalties, I think the penalty count at half-time was eight. We on average keep our penalty count to six, so that really killed us and it broke our hearts in the end.

"We had good field position and just gave the ball away through indiscipline and you can't do that against France. It had to come off at the set-piece, and the lineout was an area we've been really powerful in and given ourselves a platform to work off and it didn't fire."

Argentina? "Well I don't know, I haven't thought about it yet, but we're certainly going to go out there and give it a shot.

"Looking back on tonight, it's very disappointing. We came here with a game plan, we came here very fired up; maybe too fired up and maybe we crossed the line discipline-wise. But there were some very tough calls went against us out there and that was probably the bones of it."

Ireland captain Brian O'Driscoll also cut a disconsolate figure: "They had a huge amount to play for, just like ourselves. In fairness to them they made it very difficult for us. Our ill-discipline let us down and they kept the scoreboard ticking over. Then when they scored their try it pretty much killed the tie."

He was gracious in his words for the victors. "Credit to them (France), we didn't up our performance enough like we said we would. If you don't play out of your skin against France then you come off second best."

O'Driscoll admitted: "We need a massive result (against Argentina), I don't know the permutations: whether we need five points and deny them a bonus point, but we'll think about that tomorrow.

"For the moment we're just disappointed that we didn't put in the performance we've been talking about all week."