He said that Canada's dairy interests had been "diametrically opposed" to New Zealand's interests for 30 years, and it took "just a little bit of spine to stand up to it".
Mr Parker said Mr Groser's comments were "abrasive and arrogant".
"How does he think slagging off the Canadians using derogatory terms is going to result in a good outcome for those negotiations?" Mr Parker asked.
Mr Groser stood firm: "It's called a negotiation. And to use one of Tana Umaga's memorable phrases, 'We ain't here to play tiddlywinks'."
The minister made the comments in an interview with Reuters when he was in the US for trade talks last month.
He said that Canada's highly protected dairy industry "looks like it belongs in the former Soviet Union".
He urged Canada to open up its markets and "start to engage in a serious way" on the TPP.
Canada, which has about 13,000 dairy farmers, applies tariffs of more than 200 per cent on dairy imports.