Warren Gatland admitted Wales were forced to draw upon their reserves of character to dig themselves out of trouble in a 20-19 World Cup quarter-final victory over France at Oita Stadium.
The Grand Slam champions trailed 12-0 at one stage and 19-10 at half-time but they capitalised on the 47th-minute dismissal of Sebastien Vahaamahina for an elbow on the head of Aaron Wainwright to spring their escape act.
Ross Moriarty scored the decisive try with six minutes remaining to leave France to lament Vahaamahina's brazen act of thuggery.
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"Hats off to France because they were excellent and were very unlucky. They have definitely improved since the Six Nations," Gatland said.
"I'm very proud of our players because they never give up even when they're under a bit of pressure. They keep fighting and finding a way to get a result.
"The red card was significant but that sometimes galvanises teams as well. The last time we met in a World Cup it was very a similar score - that was a one-point game.
"We didn't play our best but we showed great character and that's testament to this group of men and now we can look forward to the semi-final.
"We're excited about where we are - the semi-final of a World Cup. (Captain) Alun Wyn Jones said it's 240 minutes to do something you'll remember for the rest of your life.
"We're down to 160 now. If you can't get excited about that then nothing will excite you."
Referee Jaco Peyper made one of the easiest decisions of his career by showing Vahaamahina a red card for his assault on Wainwright, which took place in full view of Oita Stadium.
The lock and opening try scorer spent the rest of the game unmoved sat on the bench with his hands on his head.
"The officials dealt with it appropriately. I don't think anyone could complain about that. The right decision was made," Gatland said.
"Rugby is heat of the moment stuff and he made an error of judgement. When you've got a lot of testosterone involved in some pretty high-intensity games, that will sometimes happen. He's made a poor decision."
Gatland revealed that number eight Josh Navidi limped off with a hamstring injury while centre Jonathan Davies was forced to withdraw from the starting XV before kick-off because of a knee problem.
"Josh Navidi has a hamstring but we don't know how severe it is. Jonathan wasn't far away from being right, he just made a made decision that was best for the team," Gatland said.
"We assessed him this (Sunday) morning and he wasn't 100 per cent. Hopefully over the next 48 hours he'll put himself in contention for the semi-final."
France boss Jacques Brunel endorsed Vahaamahina's dismissal and was more concerned by Wales' controversial match-winning try that saw the ball ripped from Les Blues hands before appearing to travel forwards to Justin Tipuric.
"The red card I don't contest - when you see the images it's very clear. He did have contact with the face so we can't deny that," Brunel said.
"Of course it changed the game. When you're playing half the match with 14 men it's difficult.
"I want to stress the quality and courage of our team because we had to make up for this numerical disadvantage.
"There are other decisions I'm not totally sure of. I would like to see the last try again because they grabbed the ball and it went forward. I would like to see that image again and I'm disappointed about it."
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