"It's very clear guys," Peyper told his TMO after viewing the replay of the incident. 'That's a red card".
"The first action is around the neck. Then you've taken your arm away and deliberately you've hit him with the elbow in the head. That's a red card," he told Vahaamahina, who had earlier scored a try.
It was a needless infringement by the Clermont Auvergne man, in a maul where he also grabbed the Welshman around the neck before striking him with his elbow.
"Obviously he blames himself," France first-five eighth Camille Lopez said after the defeat. "He got a red card in a quarterfinal and he left us with 14 for part of the match, so of course he blames himself. But the group won't in the slightest."
The last time the two nations met in World Cup knockout game in 2011, Welsh skipper Sam Warburton was sent off in the first half before France went onto win 9-8.
Reduced to 14 men France couldn't hold off the Welsh comeback which was completed when Ross Moriarty scored with six minutes remaining. A Dan Bigger conversion gave Wales the lead for the first time of the match.
They held on to make the semifinals for the third time and first since that 2011 defeat.
For France it is two straight World Cup tournaments with a quarter-final exit following their 2015 thrashing to the All Blacks in Cardiff.
Wales will face either hosts Japan or South Africa, who knocked them out in the quarter-final stage four years ago, for a spot in the final.
