The Glasgow flanker said: "I think after last week we were so bitterly disappointed.
"This is a step in the right direction. The belief is so strong, we are a very tight squad. We knew if we could play to our abilities we could win these games."
Fly-half Dan Parks kicked six penalties and a drop goal as Scotland bounced back in style from last weekend's 49-3 loss to the All Blacks.
Scotland coach Andy Robinson said: "We're hugely delighted with the victory.
"This victory is achieved by the players and the mindset they've brought into the week that they're able to take on anybody.
"There's something brewing but there's a lot of hard work to go on. Every time we perform we've got to be at our very best.
"We'll go step by step. We've got a long way to go. We've got to keep our feet on the ground because we play Samoa next week and that's going to be a tough game for us.
"I think a number of young players have come of age today.
"I thought Richie Gray really stepped up today, particularly when Scott MacLeod went off (with a rib injury).
"The pressure he put on the South African lineout, his defensive work and the hits he put in, but also some of his ball carries."