Gregor Townsend and Rory Darge were both left perplexed by the decision not to send off France hooker Peato Mauvaka for an apparent head-butt on Ben White in the first half of Scotland’s Six Nations defeat in Paris. The Scottish scrum-half was pushed to the ground and lying prone when Mauvaka launched himself at him in the 20th minute. The hooker was shown a yellow card, which was later reviewed by the bunker official. The decision was not to upgrade it to a 20-minute red card. Darge, the Scotland co-captain, felt the incident warranted a red card “If I'm being honest, yeah, probably,” he said after the match which France won 35-16 to clinch the Six Nations championship. “It looked like a headbutt. But, you know, that's the way it goes. You get some decisions your way, you get some not your way. It's not the reason that we lost the game, definitely not. “But I thought it should have been a red card - it looked to me like an intentional headbutt, but I've not watched it back. We've been on the right side of some decisions this campaign, and been the wrong side of some. It's not something that we're going to spend a lot of time thinking about, because there's no point, it's gone. The thing that's worth working on is what we can control.” The incident happened during a break in play and Townsend queried the logic behind the match officials’ decision-making. “The decision not to raise it to a red card was because there was not excessive force. I'm not sure that's really the criteria for a non-tackle incident,” said the Scotland head coach. “It clearly was a non-tackle incident, it was after the whistle. So, if there was head contact and that was intentional, it shouldn't be anything to do with the force that was involved.” Townsend said White was OK after the incident and refused to use it as an excuse for the result which saw Scotland finish the campaign in fourth place, behind France, England and Ireland. “I feel sorry for Ben White here, because he did nothing,” added Townsend. “He was first of all pushed to the ground, and a push is nothing in rugby, and then he got collided in the head, so I don't know how it wasn't raised to a red card, but as Rory mentioned, whether that has had anything to do with the final result, who knows, because France deserved the win, deserve to be champions, they're a quality side. Even though we played really well at times tonight, France were the better team in the end.” Townsend agreed that the bunker review system allowed referees to abdicate responsibility to a certain extent. “I think we've taken decision-making away from referees, and that's the process that we have now to speed up the game, but you don't want to miss incidents that are clearly in the book that should be red cards,” he said. The loss in Paris meant Scotland won just two from five for the second Six Nations campaign in a row, the first time that has happened during Townsend’s eight-year reign. The coach felt his team stood up to the huge physical challenge posed by France and singled out Gregor Brown for praise. The young Glasgow forward was making his first Six Nations start for Scotland. The visitors matched France in the first half, scoring a try through Darcy Graham and having another, by Tom Jordan, chalked off just before the interval because Blair Kinghorn had strayed into touch earlier in the move. If the try had stood, Scotland would have been ahead at the break. As it was, France led 16-13 at half-time and powered away in the second half. They scored four tries through Yoram Moefana (two), Louis Bielle-Biarrey and Thomas Ramos for a bonus-point win to secure the title. England, the only team to beat France, were second, one point behind. Ireland were a further point back in third place. Scotland were fourth, 10 points adrift of the new champions. “It's a difficult one because we lost the game and we weren't pushing at the end to win the game, but what we asked for the players tonight was to deliver physically,” said Townsend. “One of the biggest challenges you get in world rugby right now is the French pack, the Springboks are very similar, and then when they bring a new pack on, how you can not only withstand that challenge but be very aggressive with the way they play. “They play a lot outside of nine and they bring the forwards into the game and I thought we were very good there. “Now when you flip it around, how our forwards carried was some of the best carrying I've seen. Gregor Brown was fantastic, his first Six Nations game, he did really well in attack and defence, he did really well at set-piece. Zander [Fagerson], Pierre Schoeman, Matt Fagerson, so many players fronted up physically. “Then we had some really good parts to our attacking game, we created things and the effort was there throughout the 80 minutes. “I loved right at the end, even though the game was lost, there was a maul on our line and we were very physical with two second-rows playing their first Six Nations games and turned the ball over. There's a lot to be proud of and a lot to build on. “Strangely, our two best performances this year were what happened in defeats to England and to France, especially 80-minute performances, but we can take a lot of those two games as we look to next year and beyond when we have those challenges again.”