Britain sit third in the table with 19 gold medals while Australia are enduring one of their worst Olympics and languish in 19th place with two golds.
The 410-strong Australia team had come to London hoping to spoil Britain's party, continuing the fierce sporting rivalry between the two countries that goes back over a century.
Green said there was still time for Australia to climb the table but acknowledged Britain had got it right for London.
"Our position in the medal tally will change, but we recognise and applaud the work to date Great Britain has done, they deserve the medals they are getting," he told a media conference on Tuesday.
British and Australian sports fans take every opportunity to indulge in sledging, the dark art of unsettling opponents with well-chosen barbs and trumpeting their own success as well as their rival's failures. Green had no problem with it in London.
"When you win you can do that, that's part of being on top," he said. "We'll take it on the chin, whatever they give us, we're still very excited abut the rest of the Games."
Australia's flop in London has sparked calls for an inquest and swimming officials have ordered an independent review into the team's poor showing.
Australia's swimmers have always punched above their weight at the Olympics but have come under fierce criticism at home because they only won one gold, their lowest haul since the Barcelona Olympics, 20 years ago.
Green expected more golds to come Australia's way over the coming days with 100 metres hurdles world champion Sally Pearson a favourite. They also have big hopes in sailing.
However, he acknowledged Australian sport would have to re-evaluate how they do things.
"That may be with the way we invest our money ... a strategic approach to the way we invest our money, the way we pay our athletes, we'll look at all of that post-Games and then we'll make some recommendations," he said
"Games go in cycles and sometimes they take four, sometimes eight years to implement a strategy which has rewards at the end of it.
"We'll do what we can and implement the right strategy to ensure that we are in a position where we feel we rightfully belong, and that's in the top five on the medals table."
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