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Skrela came on in the 51st minute to replace Francois Trinh-Duc at No 10, but lasted only 11 minutes before being injured and having to go off.
Capped 24 times, the 32-year-old, who moved from Toulouse to Clermont this year, will be replaced by the uncapped Jean-Marc Doussain of Toulouse, who will arrive next Tuesday.
France's next Pool A match is against Canada at Napier on Sunday.
"We decided yesterday (Tuesday) that David would not be able to be fully fit after his injury on Saturday .. and after consulting French medical experts we got the confirmation that it would take a few weeks to recover," Lievremont said.
The 20-year-old Doussain who can also play scrum-half, captained the French under-20 team at the last age-group World Cup in Italy in June.
Lievremont said that Doussain had "caught my eye."
"I have full confidence in this player even if he has not played for me before. I look on him as the best replacement in this position," the coach said.
Lievremont said that he had hoped to have Doussain arrive in New Zealand earlier than next Tuesday but his club wanted him to play against Biarritz in a league match at the weekend.
