More than 62,000 turned out to see if Scotland could continue their 100% home record this year and beat a stuttering Aussie side for the first time in 24 years.
Comfortable wins for Scotland over Romania and Pacific Islanders in the previous autumn Tests coupled with the tourists' defeat by Ireland and draw with Wales had boosted expectations.
But despite going 10-0 ahead in a lightning start, the Scots could not cope with the power of the Aussies in the second period.
Paterson said: "We know how good and strong they were and we know how hard they were to play against.
"If people have lost respect, well I hope that's not the case, but we have got massive respect for Australia.
"It shows where we have got to go if we seriously want to compete at the World Cup.
"We know where we are. We know what we have to get right in order to get better."
Paterson revealed coach Hadden had said after last week's win that the Scots were further forward than he thought they would be.
The Edinburgh player added: "One bad result against a quality side doesn't undo all the hard work and effort we've shown in the last 18 months. If it does it's a fragile team and we are certainly not that."
Paterson, who won his 69th cap on Saturday, believes the Scots must take their chances and tighten up in the last 10 minutes, after losing two tries in the final stages.
He said: "It is execution that is hard work. We didn't really get our attacking game functioning and that's partly because you're playing against a team who starve you of ball."
With the quality of passing and strength Australia showed, Paterson believes opposing teams would have to cut off the source early on in their attacks.
"That involves taking a risk, that involves flying up but I think we approached it properly.
"There was no need for us to take a risk because our defence has not been exposed for a long time. But it was exposed because of the quality of their players."