One person described it as "disgraceful and offensive" and said a performance involving a waiata and poi would have been more suitable.
Someone added that her performance was "more of an insult" and said her "tutors are idiots for letting her do that. Big thumbs down to them."
However, Mr Te Ua, who said he was Dr Lambie's tutor, has leapt to her defence on Facebook.
"Deborah performed her heart out, she gave it her very best, I think she was very brave to put herself in a vulnerable position by exposing her wairua to the world through haka.
"Still being new into haka the execution on the day was filled with ihi and of course her technique wasn't as good as the rehearsals but I am very proud of her regardless of the negative backlash that has happened," he wrote.
"I think it is sad how we respond to people who have a genuine passion for learning and sharing our culture, but everyone is entitled to their own opinion I guess."
Mr Te Ua said he had initial reservations about helping the contestant but said "within a couple of minutes I could tell that her heart was in the right place".
"She was respectful of our culture and processes, she understood its importance to us as Maori and the pressure that would come with choosing to represent at the Miss world competitions with Maori culture."
According to Mr Tu Ua, the duo worked together for three months prior to the Miss Universe competition and in those months Dr Lambie was schooled on the origins of haka, wrote assignments on kapa haka was even taken to a marae to rehearse.
Mr Te Ua said Dr Lambie would continue to learn kapa haka and begin studying Te Reo Maori "as she is totally in love with our culture and customs" despite the negative feedback.
