Centre Jonathan Davies says Springboks coach Heyneke Meyer told the Wales team they deserved to win the second Test.
A late penalty try consigned Wales to a heartbreaking 31-30 defeat.
Davies, 26, said Meyer came into the dressing room post match and acknowledged Wales "probably deserved to win."
"It's nice when people recognise when we put in a decent performance, but it's a results-based game," said Davies.
"I thought the performance in the first 60/70 minutes was outstanding and deserving of the win.
"I was pleased to see that we bounced back from last week [the 38-16 loss in Durban], a disappointing performance and we showed today the performance we're capable of," he added.
"What we need to do is make sure that we learn how to close these games out because it's happening too often now that we're getting ahead and just letting teams back in right at the end."
Wales flew into a 17-0 lead inside 25 minutes thanks to a Dan Biggar penalty and converted tries from centre Jamie Roberts and wing Alex Cuthbert.
But two yellow cards within three minutes for lock Luke Charteris and fly-half Biggar allowed South Africa back into the match before half-time.
With Wales down to 13 men and a penalty try awarded following Biggar's infraction, the Boks reduced the deficit to three points after a Hendricks try.
A Ken Owens try early in the second half extended Wales' lead before Morne Steyn replied with a penalty for the hosts.
Another two Biggar penalties put Wales 30-17 ahead going into the last ten minutes.
South Africa full-back Willie le Roux's try, converted by Steyn, brought the Springboks within seven points.
With less than two minutes remaining Hendricks made a bid for the try line in the corner and Williams led with the shoulder.
After some consultation, referee Steve Walsh headed for the posts, leaving Steyn with a straightforward of conversion to continue Wales' 50-year winless streak in South Africa.
"The way we lost last week as hugely disappointing and today, from the jaws of victory, they snatched it away from us," Davies added.
"We would have loved to have finished on a good note, but that's the way it is.
"We need to make sure we dust ourselves off now and get ourselves ready for a big year coming."