Full-back Jamie Roberts and winger Shane Williams scored tries but otherwise the Grand Slam winners were put to the sword by the ruthless Springboks.
It was Gatland's first defeat since taking over in January and the Kiwi refused to excuse Wales' error-strewn and indisciplined performance.
"South Africa thoroughly deserved to win the game. We were well beaten and dominated by a better side," he said.
"I don't feel we earned the respect we wanted to - not just the players, but the management too. Quite frankly I'm pretty embarrassed by that performance.
"We spoke about coming here and competing physically with the Springboks but we didn't do that.
"The players will go away and see it as a big challenge to improve for next week. We're not making any excuses because we weren't good enough today.
"I don't like losing too much so I'm hurting. There are no excuses for the performance. We were well beaten."
Conrad Jantjes, Jean de Villiers, Pierre Spies and Percy Montgomery scored tries for South Africa, who bristled with intent throughout.
"Our handling was poor and our discipline in terms of the number of penalties we gave away was bad," said Gatland.
"That didn't help us stay in the game. They kept the scoreboard ticking over, which was disappointing.
"They were a typical southern hemisphere team - really strong in the collision areas.
"They dominated us physically at the breakdown, both in attack and defence, and we'll have to improve on that.
"We didn't get the rub of the green on a few passes but that's Test match rugby."
Wales were outmuscled by a bigger team and the world champion Springboks will relish the second Test next weekend after dominating the first.
The tourists have never won on South African soil - they have now lost all seven meetings - and skipper Ryan Jones demanded a vast improvement in time for Pretoria.
"We didn't do ourselves justice and were punished by the world champions," he said.
"Test rugby is about keeping yourself in the game and creating opportunities, which we didn't do.
"We have to take this on the chin and have six days to turn it around.
"We'll go away, take a long, hard look at ourselves individually and collectively. There will be a bit of finger pointing.
"We'll have to front up to a man. The breakdown was key today, we came off second best.
"It will be a long 80 minutes next week if we don't put it right."
Hooker Matthew Rees will undergo a scan tonight after sustaining an Achilles injury.