Mr Allen and Freeville School principal Paul Wilkinson said the "unprofessional" comment came when Ms Parata realised principals had not read a document about national standards that she had put online last Friday.
Mr Wilkinson and Mr Allen said this was particularly offensive for Christchurch principals who were receiving their letters regarding the fate of their schools that same day.
"She called us 'unprofessional' because we had not read something which she had put online Friday last week - the same day we were waiting for our letters," said Mr Allen.
"It was appalling to call us unprofessional," said Mr Wilkinson.
But Ms Parata yesterday denied she had called principals "unprofessional". She told The Star that Mr Allen's and Mr Wilkinson's assertions were "absolutely untrue".
"I actually received plenty of positive feedback from that conference and had one on one time to listen to the principal from Manning Intermediate and the principal from Te Whanau Tahi."
However Mr Allen was adamant about the heated nature of the conference.
"If you ask her a difficult question all she does is shout at you, it was pretty eye-opening," he said.
He compared it to the highly publicised PPTA's national conference on Wednesday where Ms Parata was accused of being "patronising" because she said teachers needed to pronounce Maori and Pacific Island pupils names properly.
Mr Allen said Ms Parata's tone and manner was "embarrassing" at the conference.
He said he had little faith in the ministry's promise of meaningful consultation in Christchurch after seeing Ms Parata in action.
"I have very little faith in the consultation that the ministry say they are going to do after seeing the minister at that conference - the feeling that came out of it was 'it's my way or the highway'," said Mr Allen.
