The Tongans triumphed 19-14 in Wellington on Saturday in what was one of the biggest upsets in World Cup history, but it was still the French that made it through to the quarter-finals from Pool A where they will play England.
Lievremont, who has endured a torrid campaign to date in New Zealand, said that "every missed pass, every missed tackle I felt like a deep personal failure."
"We always hope for better. Even if so far our campaign has been anything but straightforward, I had the feeling that the players were making progress and that what was at stake in this match - qualification and a place in the quarter-finals to come - would have put us out of danger of this kind of mishap."
"The French rugby world and my players mocked the footballers last year, but in some ways yesterday we never got off the bus," he added, referring to the players' revolt against coach Raymond Domenech at the 2010 World Cup when they stayed on their team-bus when they were supposed to be training.
Lievremont, who has already been told his contract will not be renewed at the end of the World Cup, said that he also regretted that his players had gone their separate ways after the defeat.
"I would have preferred it if we had shared a glass, spoken about it and just agreed that it is still a fine adventure," he said.
"I've got respect for them and think highly of them, I talk to them openly. I think it is reciprocal even though I am under no illusions.
"We live in a society where image matters. I saw players with their agents on the eve and after the game instead of regrouping as a team."
Turning to his own position, Lievremont, who took over as France coach after the last World Cup four years ago, said that he was fully aware of his own failings.
"As many people believe, I am certainly no more that a division two coach, who is incapable of coaching a team as fine as France.
"Some compare me with Raymond Domenech. You must know that I have got an immense respect for him.
"He did fight. I know what that means and, I repeat, I have absolutely no intention to give up.
"If we fail again next weekend (against England), you have your scapegoat, but what people think about me is not important.
"I am still convinced that we have the potential" to beat England, he added.
There was more bad news for the French with the news that veteran centre Aurelien Rougerie could miss the rest of the tournament with a serious shoulder injury.
Skipper Thierry Dusautoir also picked up a shoulder injury, but it was believed to be less serious than that of Rougerie.
Lievremont had words of comfort for his captain who has come in for criticism for his leadership skills.
"I want to give Thierry Dusautoir a message. Only he is exemplary. He spends a lot of energy to mobilise his troops. He is heavily criticised. He should only focus on his performance," he said.