The national team coach hailed a few "good" individual performances from Danny Fox and Alan Hutton as Jordan Rhodes scored on his first start for his country
The home team initially fell behind when Mark Bresciano hit a stunning volley from 25-yards, only for highly rated youngster Jordan Rhodes in equalise on his first start for his country.
The second half saw Australia's Jason Davidson inexplicably head into his own goal to put Scotland ahead, before Ross McCormack settled matters late on.
Levein told BBC Radio Scotland: "We played like a proper team and deserved victory,"
"People have been doubting us and I don't know why. We had one bad performance in the States and the lads themselves were hurting more than anybody about that."
The national coach also praised the likes of Jordan Rhodes, Alan Hutton and Danny Fox: "His [Rhodes'] one-touch finishes are incredible so if you don't put the ball in the box, he's not going to get a chance to score."
"I have to compliment Danny Fox and Alan Hutton. They put some great balls into the box."
The win takes Levein and his men into next month’s World Cup qualifiers on a high after being thrashed 5-1 by the USA in May last time out.