But he warned that only "half the job" was done as they now aim to top Pool C and potentially set up a quarter-final clash against Wales.
O'Driscoll told ITV1: "It's a performance we knew we had in us.
"We had to dig deeper than we had done in the last five games."
Ireland experienced an indifferent preparation for the World Cup, with some poor displays in their warm-up games.
But they displayed a fighting spirit and confidence against a well-fancied Australia side.
"It's half the job done," said O'Driscoll. "Two wins and two more to get. As much as we will enjoy this, let's not lose sight that we have two more games."
Ireland coach Declan Kidney also refused to get carried away with the victory.
He said: "I was pleased with the way we went about out business.
"We managed to stifle a very good Australian side.
"I think our scrum is getting a little stronger. We still have a little bit of work to do. The work really starts now."
He did, however, add: "It's the fifth time we have played Australia in the Rugby World Cup and you get a bit fed up with losing."
Paul O'Connell admitted it was a "special day", but also refused to get carried away.
"Today we played to our potential," said the lock, who captained the Lions on their tour of South Africa in 2009.
"It's just a pool game for us. All the games from now on in are big games."
Australia coach Robbie Deans said: "Ireland were very effective. They defended really well and did not allow us to recycle the ball. It was effective.
"We would have liked more field position. Our decision-making was not always great."
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