Ireland coach Eddie O'Sullivan said his players were right to keep the match going in stoppage-time despite conceding a crucial late try to Italy.
Gordon D'Arcy scored one of the Irish tries against Italy
The Irish won 51-24 but the winning margin proved insufficient to beat France to the Six Nations title on points difference.
"In this situation you should never die wondering," said O'Sullivan.
"We cannot change it now and I would not want to change it. I am very happy with that performance."
We could wallow in self-pity now, but I don't think that would be the right thing to do
Minutes after the final whistle in Rome, France went into their match against Scotland knowing they would have to win by more than 23 points to snatch the championship.
And the French clinched the crown in a knife-edge finish, getting the title-clinching score in stoppage-time in Paris.
"It's hard to take, but that's sport. We could wallow in self-pity now, but I don't think that would be the right thing to do," added O'Sullivan.
"We've won four out of five matches, played some great rugby and scored some great tries. We have to kick on from here."
Ireland winger Denis Hickie admitted they had doubted if their winning margin against Italy would be sufficient.
"It was a strange feeling in the dressing room when we came off," said Hickie, one of the Irish try-scorers.
"We scored as many points as we could, and we won the match, but we still came off feeling that it might not be enough.
"We thought we had to keep on playing and we did that.
"Eddie came in and said we were right to keep playing to the end."
Centre Gordon D'Arcy was happy with the way his side played.
"We knew we had to score tries and put Italy under the screw from the word go but we were disappointed to let them in for two tries at the end," said D'Arcy.
"The crowd were great though. We have always said the Irish fans are some of the best in the world."
Ireland's victory was marred by a hamstring injury to captain Brian
O'Driscoll, who had to be helped from the pitch in the second half.
"Brian has a serious hamstring strain," O'Sullivan added. "We don't know the extent of the damage but he's in a lot of pain.
"We'll go back to base and see what the damage is, but it doesn't look great at the moment."