Australian Defence Minister Stephen Smith said he believed Anderson would regret the remarks.
He said they were "disrespectful" to those who fought from both sides of the Tasman.
"We have the highest regard for the contribution made by our New Zealand colleagues - as they do have for us. Anyone who has been to Gallipoli, who has been to the New Zealand monument at the top of the hill, who understands the contribution that our Kiwi brothers and sisters made in Gallipoli alone - let alone other conflicts, including and up to Afghanistan - would dismiss those comments with the disrespect they deserve."
Anderson yesterday told One News the response to his comments showed "how thin-skinned they are".
"We shouldn't have a situation where, because we are New Zealanders, we can't comment or criticise anyone else."
Anderson said his comments "in no way" denigrated the sacrifice made by Australian soldiers.
But the New Zealand Returned and Services Association came out in support of their Australian counterparts.
Chief executive Stephen Clarke - a military historian - said the comments were historically inaccurate and disrespectful to the memory of those who served and died from both New Zealand and Australia.
"Australian and Kiwi servicemen and women have served side by side for over a century and RSA members will be disgusted by the disrespectful criticism ... just days out from Anzac Day."
Anderson's comments were made during an April 19 discussion on Bully Beef and Balderdash, by former Australian army officer and Department of Veterans Affairs historian Graham Wilson.
- Claire Trevett, APNZ, AAP