Les Bleus needed a late try from wing Vincent Clerc to salvage the losing bonus point required to secure second spot in Pool A behind New Zealand and a last-eight date with England after a 19-14 defeat.
But it was a ragged performance by the lacklustre French, who slipped off too many tackles and gave away ill-disciplined penalties as Tonga took the game to them.
"I don't think we can be happy with this qualification," said the embattled French coach. "It's a bitter qualification but we have qualified.
"This week will be very important. We've had two defeats from four (pool) matches. I think it will be the first time a team has qualified with two defeats (in the professional era)."
Lievremont, who again denied there was any unrest and unhappiness within the French camp, implored his players to show more fight in the knockout stages.
"I trust my players. I want them to fight better. I want them to be more accurate," he said.
"I don't think we need to dwell or analyse the technical aspects of the match now. I want them to react and refocus on those values I've already talked about.
"We have no choice. We're still alive. We're still part of this adventure and I still want to fight and I think my players still want to fight too even though they are disappointed after tonight's performance."
After an abject campaign in New Zealand so far which has seen them earn scratchy wins against Japan and Canada and lose to the All Blacks and Tonga, captain Thierry Dusautoir felt his side could defeat England in the last eight but only if they improved drastically.
"After such a defeat like this the group is really upside down but we are going to try and refocus on the quarter-final," said the despondent skipper.
"We are capable of beating England but if we go on playing like this against England we're going to lose and we'll go straight back to France.
"The group will have to strengthen itself and this is going to be difficult after today. But we still have a quarter-final to play."
He added: "When you saw the performance we had tonight you might wonder what's going through our heads but we have been nervous for some time and I think that has played a role.
"But in the quarter-finals we've got nothing to lose because we will be the underdogs. We have to be aware of that and we have to get rid of our inhibitions."
Dimitri Yachvili, who kicked his side's remaining nine points, admitted he could not explain why the players were so unsure of themselves.
"We would like to have the answers for that but I don't know," he said. "It's hard. It's a hard time for us right now.
"But we are in the quarter-finals and we have to forget this game quickly. We will not give up. We will keep working very hard."
Tonga coach Isitolo Maka, meanwhile, hopes his side's superb win will result in more Test matches against tier-one nations in the future.
When the Tongans faced New Zealand in the World Cup opener last month is was the first time they had played one of rugby's major nations since the previous tournament in 2007.
"This win has really helped Tongan rugby for moving forward and I hope the IRB will give us a Test match against a tier-one country," the former All Blacks loose forward said.
"For us to beat France tonight is very special and it's good for Tongan rugby and for our people who have supported us since we have been here (in New Zealand).
"All the Pacific Island teams have done so well. Samoa did a great job last night against South Africa and while they didn't win it did really help us."
Given the size of his side's accomplishment at Wellington Regional Stadium, Maka looked the picture of calm when he fronted the media.
"The win tonight, you people don't know what it means to me and to our people back in Tonga," he said.
"In Tonga right now our people are going crazy. We are going to get a lot of support when we get to Auckland tomorrow.
"I think this World Cup has really come alive, especially with our fans who have really supported us and have been everywhere.
"I just want to take my hat off to our fans who have supported us to the end."
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