Denmark captain Daniel Agger slotted home a 32nd minute penalty and substitute Andreas Bjelland struck from close range in the 68th minute to secure the win for the home side.
The result ensured that Princess Mary, who was in the crowd at Parken Stadium, did not have to worry about her loyalty being tested in front of her subjects.
Australia had chances but the industrious forward combination of Harry Kewell and Alex Brosque failed to convert in the cool conditions against their Euro-bound opposition.
"Forget the scoreline, it was a good hit-out for us," Neill said.
"What you don't see is that we have had a really physical week looking a bit further (towards Oman).
"Two avoidable goals, we created lots of chances. No injuries, match fitness. We are not going to panic."
The Australians fly out on Sunday to Oman for the opening match of the final stage of World Cup qualifying in Muscat before heading home for the June 12 clash against Japan in Brisbane.
Coach Holger Osieck used the match to test out some combinations with Jade North handed a start at right-back and Matt McKay at left-back.
A-League players Archie Thompson and Kewell were both in the run-on team.
After a shaky start by the visiting team, the Socceroos started finding their way before midfield wizard Christian Eriksen unlocked the Australian defence with a beautifully-weighted backheel.
The ball had just enough pace to go beyond Australia's central defender Matthew Spiranovic but still isolate goalkeeper Mark Schwarzer.
In trying to cover surging Danish and Liverpool defender Agger, Spiranovic was ruled to have brought him down in the area.
The Danish skipper stepped up and smashed his penalty kick to Schwarzer's left.
With Mark Bresciano demonstrating his value to the team in midfield, Australia dominated the early part of the second half and Kewell and Brosque should have delivered an equaliser.
Osieck started making changes halfway through the second half and it was around that time Australia conceded another.
The team failed to clear a corner and from a rebound, the ball dropped at the feet of Bjelland who knocked the ball home.
The scoreline could have really become unflattering for Australia a couple of minutes later when a horrible Spiranovic back pass put Nicklas Bendtner through only for the big striker to shoot wide.
