Australia have made more headlines off the pitch than on it so far during the Champions Trophy in England, with David Warner having to issue a grovelling public apology for the bar-room attack on Joe Root. His punch on the England batsman landed him a £7,000 fine and a suspension until the start of the Ashes.
Nielsen coached the side from 2007 to 2011 and had senior figures like Ricky Ponting at his disposal. He told Radio 5 Live's Sportsweek programme: "Probably the biggest difference between a lot of great sides is that strength of leadership of your players."
He continued: "It doesn't necessarily mean they have to have captain next to their name. They (experienced, senior players) expect behaviour and they understand what is expected of them, just through experience. They see young players jumping out of line they quietly and quickly jump in to ensure they straighten them up.
"That's maybe one of the tough things for this side at the moment. They don't have a lot of natural leadership around the group, apart from the actual nominated blokes who have got captain and vice captain written next to their names."
Ponting is currently excelling for Surrey in the LV= County Championship, having retired from international cricket last year. Nielson reckons he would be able to restore authority to the Test team, but admits he is unlikely to go back on his decision.
"There is no doubt he would help in that regard, having those sort of players around certainly helps," he said. "It's easy to say from the outside in he would be a good leader of the group and I'm sure he would be, but if his heart's not 100% in it it's probably too much to ask of him as well."
Meanwhile, Australia head coach Mickey Arthur has admitted that it would be a risk to select Warner for the first Ashes Test beginning on July 10. The 26-year-old's suspension means he can play no competitive cricket before the series begins and the South African coach admits that makes him an unlikely choice at Trent Bridge.
He told www.cricket.com.au: "He wouldn't have had a lot of cricket, he will have had a lot training, mind you, but no cricket.
"We've got plans to give him some centre-wicket practice etc, but it would be (a risk to play him in the first Test) and I guess it's a chance for the other batsmen in the squad to step up in the first two practice games. Because if they do that, they're likely to start in the first Ashes Test."