Connolly believes seven Test matches in the last nine weeks have taken their toll on the Wallabies, who came from behind to beat the Springboks at Sydney's Telstra Stadium thanks to a late Stirling Mortlock conversion.
The hosts were again under pressure at the scrum, while their
line-out was also below-par against the world class South Africa jumpers.
Australia also lacked attacking enterprise in the backs and were regularly out-muscled at the breakdown, much in the same way as they were in last weekend's defeat to New Zealand.
"Playing seven Tests in nine weeks has been very draining. We were flat tonight and off our game," said Connolly.
"I was disappointed how we played at times but delighted with the win. Any time you beat the Springboks, you have got to be happy. The good thing is we gutsed it out.
"We were emotionally and physically flat after last week's game against the All Blacks. After beating them [South Africa] 49-0 a few weeks ago, I suppose some guys may have thought we would have just had to turn up to win."
Connolly's views were echoed by captain George Gregan, who admitted the team was flat at training on Wednesday and struggled to lift themselves before kick-off.
"Back-to-back Tests are hard to get over," Gregan said. "Last week's game was physically demanding. But the pleasing aspect was that we showed composure and ground out a win.
"We found it hard to get into any rhythm and made some fundamental errors."
After dissecting his side's performance, Connolly immediately turned his attention to their next Tri-Nations match against the All Blacks in Auckland on August 19.
"We have two weeks to prepare for this game. Some players are thinking of Auckland now," he said.
Saturday's win was the second time Mortlock has kicked a late goal to boot the Wallabies to a Tri-Nations victory over South Africa.
Six years ago, the centre landed a penalty when Australia captured the title with a thrilling 19-18 win in Durban.
Recalling his conversion of Mat Rogers' 75th-minute try, Mortlock said: "These are the moments you enjoy - the kick to win the match. They are what you train for and you have to trust your technique and do the job."
The Springboks' Tri-Nations hopes will hinge on a Wallabies victory in Auckland.
A New Zealand victory will guarantee them the trophy and South Africa coach Jake White admits he'll be praying for an Australian victory.
"I'll be wearing my yellow jumper," he joked.
But White wasn't laughing about Saturday's agonising defeat.
"The game got away from us with four minutes to go," he said. "Had we got the bounce of the ball, we would have won.
"It was a game of inches. They hit the pole with the Rogers conversion and had Butch James' kick bounced one metre left or right when Mark Gerrard scored, we would have scored."