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Cory Jane and Israel Dagg crossed in quick succession in the first half before Dagg added his second at the start of the second.
Maxime Mermoz and François Trinh-Duc grabbed opportunistic tries as France threatened to make it respectable but Sonny Bill Williams’ late effort sealed the win.
Lièvremont said: “This match leaves me with lots of regrets. In the first half in particular we conceded three tries in a quarter of an hour making major defensive errors after a good but scoreless start. We let the All Blacks take control of the scoreboard and the game too quickly.
“The talent of the All Blacks punished us on several actions.”
France had made the brighter start with Damien Traille and Louis Picamoles both coming close to scoring, but it was Thomson who broke the deadlock as he finished off a move started by Ma’a Nonu’s searing break.
That seemed to affect the French morale and Jane went over untouched after a delightful inside ball from Piri Weepu before Dan Carter ghosted through to set up Dagg’s first try.
Dimitri Yachvili managed one penalty to make it 19-3 at the break but the All Blacks came flying out of the blocks after the interval with Dagg scoring his second virtually from the kick-off.
Carter then threw a speculative pass which Mermoz collected to race over before Trinh-Duc dived over for a controversial score after a quickly taken penalty by Yachvili.
But the All Blacks weren’t to be denied as the French failed to deal with a restart and the ball was spread wide to Williams who crossed in the corner.
Despite the defeat which leaves France still in need of one more point to guarantee a quarter final spot, Lièvremont felt there were some positives to be taken from the game.
He added: “There were some interesting things. Thankfully. I think there has been progress. I’m certain of it. We feared the worst as soon as they got away and there was a missed tackle. It was difficult to remain calm but we didn’t fall apart.”