Just a week after they suffered a 32-12 loss to the All Blacks in Christchurch in the tournament's opening match, the Wallabies inflicted the second biggest defeat in South Africa's history in Brisbane.
Connolly, however, has urged caution, insisting his team will have to improve if they are to tame the All Blacks in the same city on July 29.
"It definitely gives us confidence but equally we're aware we need to tighten up our game," he said in Sydney's Daily Telegraph.
"We had a brief chat in the dressing room later about what this meant to the team. But when the All Blacks come here, we have to be better.
"The boys celebrated the win into the wee hours and we're very happy with where we are at the moment.
"But we're just battlers. Hopefully we can improve again."