Wales were leading 3-0 when Warburton controversially saw red for a 'spear tackle' on Vincent Clerc before the French moved into a 6-3 lead at half-time.
Another Morgan Parra penalty extended the gap to six before Wales scrum-half Mike Phillips darted over only for replacement fly-half Stephen Jones to miss the conversion - leaving France with their noses still ahead.
As the clocked ticked down Wales, despite their numerical disadvantage, nearly clinched the win and a Leigh Halfpenny penalty from just inside the French half fell agonising under the bar.
But despite making few friends on their way to the final, Lievremont is just happy to be one win away from a first French World Cup crown.
"I'm going to tell you something," said Lievremont.
"I don't care that the match wasn't pretty, that we had some luck and that the Welsh deserved better.
"We are in the final and that's all that counts. If we are to be world champions playing that style of rugby, we'll be world champions playing that rugby.
"For the last few months we've been lacking lots of things, except we are in the World Cup final."
Meanwhile, Les Bleus captain Thierry Dusautoir was mindful of the fact that his side must improve if they are to take the William Webb Ellis Trophy to France for the first time.
France will now play either hosts New Zealand or Australia in next Sunday's final - and Dusautoir pointed out their most recent matches against both sides have not exactly gone to plan.
"I'm really happy to be in the final but also conscious of what we produced today. In spite of everything we need to reach this stage of the competition," said flanker Dusautoir.
"Whoever the opponent is next week, one put 60 on us in November, the other 40 three weeks ago.
"It will be a huge game for us. All the more so because of how close it was today. In a way we are lucky.
"There are a lot of people who it bothers to see us in the final. We perhaps aren't that talented, but we have a lot of heart. From today we can say it's enough to reach the World Cup final."