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Wales boss Warren Gatland admitted his players were devastated after their defeat to South Africa in the World Cup quarter-finals.
Gatland's side led 19-18 with five minutes left at Twickenham but Springboks captain Fourie du Preez dived over to seal a dramatic 23-19 victory.
It means Wales' World Cup dream is over while South Africa go through to the semi-finals to face either France or reigning champions New Zealand.
"Sum up my emotions? That's a dumb question. How do you think we are? We're absolutely gutted," Gatland said.
"We're proud of the performance but if you ask about the emotions that's not something I want to talk about.
"The guys put their bodies on the line, gave everything. That's all we can ask of them but we weren't good enough to hold on for 80 minutes.
"Credit to South Africa, they stayed in the game but we're very disappointed."
Gareth Davies' first-half try, created by an excellent kick and catch from Dan Biggar, looked to have set Wales on course for only their third win in 31 Tests against South Africa.
Indiscipline at the breakdown, however, allowed the Springboks to stay in touch as Handre Pollard kicked 18 points before Du Preez's late contribution.
"I couldn't have asked any more of the guys," Wales captain Sam Warburton said.
"From an effort point of view, we have no regrets.
"But 12 points in the first half after we gave away four penalties, all when we weren't under very much pressure, for me those were the most crucial points we gave away.
"It's essentially two tries. Other than that they didn't really stretch our try-line so to give 12 points away like what was disappointing."
Wales appeared to be a team that could threaten the latter stages of the tournament after coming through the fearsome Pool A with Australia, thanks to a stunning win over England.
"Wales can be very proud of these players," Gatland said,
"Coming out of that group, which was so tough, and that group set us up pretty nicely for what we knew was going to be a tough game today.
"They've given a 100 per cent, we saw that today, they've spent themselves, so I'm very proud of what they've delivered."
Warburton added: "It just wasn't to be today. The changing room obviously at the end was very quiet.
"At that time it's difficult to find the words. It's just sinking in that we're going home tomorrow."
The victory continues South Africa's impressive resurgence since their shock opening defeat to Japan and the 2007 champions will be confident heading into the last four.
Du Preez's try was a moment of true quality as Duane Vermeulen peeled off the scrum before feeding his team-mate with a superb backhanded pass.
"I would like to kiss Fourie, especially after that try," South Africa head coach Heyneke Meyer said.
"I've worked with him since he was 19 and he's the most astute rugby player I've ever coached. He's a tactical genius.
"If you look at South Africa playing well in so many matches Fourie is the guy organising the team, making tactical decisions.
"He doesn't always get the credit for that and I'm very happy for him."
Wales were the more creative side in the first 40 minutes but the Springboks dominated after the interval and Du Preez admitted he felt their opponents tiring as the contest went on.
"There was a stage when I thought it was really tough to break their line," Du Preez said.
"But around about 60 minutes I could sense a few of their guys were slowing the game down and I thought they were off their feet.
"We had a lot of gas left and I thought if we kept on pushing we would get through. Luckily we did."