Ireland manager Martin O'Neill complained that France had far more time to prepare for Sunday's second-round 2-1 defeat of the Irish than his squad.
The hosts, who battled back from a goal behind, had a week's rest after a goalless draw with Switzerland in their final group match, while the Irish had three days less to recover after their defeat of Italy.
"Three days is an incredible amount of time one side could have as an advantage over another," he said.
"I know we knew that before but we definitely got the short straw in that aspect. That said, France are a really, really fine team and good luck to them in the tournament."
The Irish squandered their early lead in the space of only three second-half minutes when Antoine Griezmann struck twice to send the French towards a quarter-final against the winner of Monday's game between England and Iceland.
"If we had been able to hold on for another six or seven minutes, we could have perhaps used that to our advantage with France maybe getting a little bit panicky," O'Neill told a news conference.
"I know that's a long time in a game but I'm disappointed considering the position we got ourselves into during the course of the match.
He added: "The players could not have put anything more into the game. They have not an ounce left and I am very proud of them."
O'Neill paid tribute to the Irish fans who treated the players to a 10-minute standing ovation after the final whistle.
"The feeling among the players is that it's been a splendid tournament because the fans have been wonderful in the four games that we've had," he said.
"They gave the players extra energy if there is such a thing. I could not be more proud of the fans. They have behaved themselves brilliantly and have been a credit to their country."
