"Even though we spoke about confidence and self-belief, I don't think we demonstrated it on the pitch," he said.
"You see players coming onto the ball who were confident in the Six Nations but today when those players got the ball they were looking up to see who was going to tackle them, a bit like startled rabbits in the headlights. But that is what you learn from these occasions."
Wales, who have never won in South Africa and only beaten the Springboks once in their history, were in touch as they trailed 22-10 at half-time.
"South Africa thoroughly deserved to win the game. We were well beaten and dominated by a better side," said Gatland.
"I don't feel we earned the respect we wanted to - not just the players, but the management too.
We can't throw in the towel. We have to improve before next week
But the hosts cut loose in the second period as they completed a four-try romp in Peter de Villiers' first game as head coach.
"There were a few opportunities we didn't take and a few soft penalties that we gave away," Gatland added.
"In the first half we could have been in it if we took those chances. We must be more accurate.
"We scrummaged well but the line-out didn't function, we were disappointed with our discipline...we deserved that score-line.
"But we can't throw in the towel. We have got to go away and improve those things before next week. There were a lot of lessons for us to learn."
Wales captain Ryan Jones said: "We made too many mistakes. South Africa capitalised whenever we lost possession, but we have no excuses."
South Africa captain John Smit, leading the Springboks for the 50th time, was critical of his team's defence but welcomed the debut victory of coach Peter De Villiers, who was under intense pressure ahead of the game.
"It felt phenomenal, and it's the start of a new era for sure," said Smit. "Peter can get some sleep at last."
De Villiers said: "It wasn't easy going for us, but I'm very happy. The guys didn't look so good early on, but they picked themselves up in the second half.
"We'll bank this one and live from here. But there is some hard work ahead of us."
Shane Williams said of his consolation try: "I saw Bryan Habana coming, and used his speed to get inside him.
"There was no way he was going to be able to turn around at that speed."
Wales could be without hooker Matthew Rees for the second Test in Pretoria on Saturday. The Llanelli Scarlets hooker is due to undergo a scan after sustaining an Achilles injury.
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