Wales ran them close despite losing the likes of Jonathan Davies, Liam Williams and Adam Jones to injury inside the first half an hour and Meyer admits he was delighted to see his side get over the line.
"It could have gone either way. We were very focused and very disciplined and to score three tries to nil is something I'll take any day of the week," said Meyer.
"Wales are a quality, quality side. Most of their players showed that in the Lions series. Any away win is a great win, especially scoring three tries and conceding none against an unbelievable attacking side that have shown what they can do.
"Wales did well in the second half but we kept our defensive lines. Jean (de Villiers) did well as captain and a lot of the youngsters came on and made a difference. We used every single chance that we had and you could see the experience in the side - I never felt there was any panic.
"We kept our cool: at one stage the guys were really under pressure but they came through and won by nine points, which I would have taken before the match as I was really worried about this game."
Meyer highlighted his side's tactical kicking, defensive heroics and their physicality as the central factors in a 14th straight win over Wales.
The former Leicester boss was quick to praise the Boks' ability to adapt to northern hemisphere conditions and he is convinced they are on the right track ahead of Saturday's trip to Scotland and the following week's clash with France in Paris.
"I always knew this was going to be a totally different challenge and we would have to be more astute tactically. It's a totally different game over here," added Meyer.
"We're starting to adapt. This isn't like the Rugby Championship: you can't play from scrums and you don't get any quick ball. Our tactical kicking was much better and that was probably the difference on the day.
"I'm very proud of the guys. It was a really tough encounter. We always knew it was going to be very physical out there. We made a huge step up in our defence as we weren't happy with that in the Rugby Championship.
"We've got a very big, physical pack of forwards who can score tries but can also be very good in the septpieces. I thought we were brilliant in the maul and we were brilliant in defence. We're getting the balance right where we can still score tries but we can also outmuscle teams."