Handre Pollard's penalty sent South Africa through to the final, but Warren Gatland insists Wales left nothing out on the pitch in Yokohama.
Wales could not have put any more effort into their display against South Africa, according to Warren Gatland, who took pride in his side's over-achievement at the Rugby World Cup.
Handre Pollard's late penalty settled a tense semi-final in Yokohama on Sunday as the Springboks came out on top 19-16 to progress to the final, where they will face England.
Next Saturday's clash will be a rematch of the 2007 final, which South Africa won 15-6, while Wales will face New Zealand in the bronze match on Friday.
Josh Adams' converted try had put Wales level with under 15 minutes remaining, but the Six Nations champions failed to capitalise on some sustained pressure, with Pollard settling the contest with his fourth successful penalty with four minutes left.
Gatland, though, was adamant his side had little else left to give.
"We gave 100 per cent. It's a tough, physical South Africa team, they won the collisions in terms of the carry and stuff, but I thought we were pretty good at times, but they're big men," Gatland, whose tenure will come to an end after the World Cup, told ITV Sport.
"Our guys didn't take a backwards step and I can only be proud of them for that and like I said we stayed in that arm-wrestle for a long time.
"Great credit to South Africa, they played very well, and we probably gave up too many penalties in our own half and that cost us dearly.
"I'm proud of the fact we never gave up and that got us back into the game and we were in the arm-wrestle, but probably three or four penalties during the game, which would cost any team points...
"That's how close and tight these games are. We're disappointed because we worked hard, and a penalty is the difference between the teams.
"We've punched massively above our weight when you consider the playing numbers in Wales. I'm massively proud of what these guys have achieved – they'll keep playing hard and working hard.
"For a long time, it was pretty close and at 16-16 you're dreaming about the points going the other way but congratulations to South Africa and I'm sure it'll be a great final with England."
Gatland's counterpart Rassie Erasmus, meanwhile, believes the Springboks' grit and spirit will ensure they have earned the respect of fans back home and across the world.
"We're in the final of a World Cup. I guess that'll get some respect, but we're only halfway there," he said.
"We play a class England team in the final but we're there, we've got a chance now and we might go all the way, you never know.
"Our group stands together. Nobody cares who gets substituted. We substituted our captain and he takes it on the chin. The guys defended on the try line and those moments count and really help the team gel together and that kind of team spirit can make the nation proud."
