Alastair Kellock took the Australian-born lock's place in the starting line-up while James Hamilton was released from Leicester duty to take his place on the bench.
Hadden said: "Obviously we'd rather it hadn't happened and it was one of a number of problems that we have had to deal with over the past few weeks - there have been a number of injuries.
"But we're no making any excuses, that's what happens in rugby. We just have to find better ways of dealing with it.
"We'd obviously far prefer to have these problems now rather than in the World Cup and we'll go back and look at how we've dealt with them and hopefully come up with better solutions next time.
"We're just thankful to Leicester for coming up trumps and releasing James Hamilton. He was down to play in their side against Wasps this weekend but we are grateful to Pat Howard (Leicester coach) who agreed to release James for the game."
Scotland started the match brightly with an early try for Simon Webster but the Wallabies hit back impressively as Stephen Larkham, Stephen Moore, Chris Latham and Mark Gerrard all crossed, the latter on two occasions.
The defeat ends Scotland's unbeaten record at home in 2006 and provides a reality check for the revival under Hadden.
He said: "The first thing to say is that we were well beaten by a good side who performed better than us on the day.
"Australia came back at us very well after our excellent opening and our accuracy wasn't quite there to beat a side as good as Australia.
"We haven't had the best three weeks in terms of preparation for this game but there's no excuses because we still believed we were capable of doing something special today.
"But I still believe we have made progress over the last three weeks. It's enormous progress to get over 60,000 Scottish people to come to this game.
"It's just disappointing we couldn't give them the special result they wanted. Having said that it is excellent preparation as move towards the World Cup and hopefully we can learn from this game."