Speaking to Planetrugby.com after the match, the 127-Test veteran said it was a disappointing way to play his last outing at the hallowed South African ground.
"We created enough opportunities to snatch a win, but the details weren't there in our work," Gregan said.
"They (South Africa) have a good scrambling defence. They work hard and they make you work hard to get any points, so when you get opportunities you have to take them."
"We suffered from that (not taking the opportunities), and we're the team on the wrong side of the scoreboard."
Gregan also commended the hosts for upping the ante in a tense second half.
"At half-time we knew we were in it," he said.
"It was a very fierce contest and we knew it would come down to who would control possession and take their opportunities in the second half."
"They got off to a good start with some brilliant goals and a good try, but we showed a lot of character to bounce back and making it a three-point ball game."
"But they got away with it in the end, so it was disappointing coming here and not having a good final result to the season."
Wallabies head coach John Connolly echoed the sentiments of his skipper and highlighted his team's poor ball control as an area in need of improvement.
"I guess we are really disappointed with the result," Connolly said after the loss.
"Our execution let us down. We had a few borderline calls, but we trained very well this week and gave ourselves the best chance possible."
Despite a disappointing end to their 2006 Philips Tri-Nations campaign, Connolly said there were numerous positives the Wallabies could take from the fierce encounter.
"Positives are our line-out competed well and there was no lack of effort, but we just didn't gel," he said.
"We are, however, delighted with our progress in the Tri-Nations. We can take quite a bit from the competition."
"We probably played a bit flat and they put us under pressure. We gave away too much ball at the back of the line-out, but we have no excuses and it just shows that South Africa are difficult to beat here especially at altitude."