The Wallabies, 1/5 favourites to win the match, were beaten 15-6 at Eden Park on Saturday as an unpredictable tournament produced its biggest upset.
It was Ireland's finest World Cup victory and Gaffney admits it was overdue.
"Winning in the southern hemisphere is not something we've done a lot of, so we regard that as a monumental win," Gaffney said. "It was an enormous performance and everyone was of the same opinion.
"The boys knew they had it in them and there were some very emotional chats in the build up week, including from some guys not in the 22.
"We had to go out and start showing what we can do. We couldn't start wandering through the World Cup and not perform. Against Australia we put it on the paddock.
"I don't know if the Wallabies underestimated us. I don't know whether they did show us enough respect, I'm not quite sure there."
Ireland have two remaining pool games against Russia and Italy and Gaffney insists they are refusing to contemplate the knockout stages until those games have been negotiated.
"Brian O'Driscoll's address after the game was very pertinent. He said we're only 50% of the way," Gaffney added.
"We're not treating anyone with disrespect, it's not an Irish thing. We'll go out and pay everyone the respect they deserve.
"We haven't qualified from our pool yet, we've still got two games to play.
"Russia are a growing side. Every time we play Italy it's a sticky game, it's never easy whether it's home or away.
"They're confrontational and have a great set piece. It's going to be a great Test for us."
Paul O'Connell and Gordon D'Arcy sustained hamstring strains against the Wallabies, but have yet to be ruled out of Sunday's clash with Russia in Rotorua.
"The progress of both players will be monitored over the coming days," read an Irish Rugby Football Union statement.
"No decision on their availability for the game against Russia will be made until the team is announced on Friday."
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