''I was disappointed," Taumaunu said.
''I thought there were too many errors, and was disappointed in the number of offensive penalties. Those are things we need to tidy up."
World No 5 Malawi had the outstanding figure on court in the Tactix goal shoot Mwai Kumwenda, who was largely responsible for Malawi making 47 of their 51 shots at goal, compared to New Zealand's disappointing 50 from 60.
"I thought Malawi were impressive yesterday against Northern Ireland and we are pleased to be through that," Taumaunu said.
Captain Casey Kopua sat out the first half and defender Katrina Grant was playing her 50th international.
Asked what she liked about New Zealand's performance, Taumaunu took a long pause, then: ''There was pressure and we did come through it. I think we put ourselves under it, but we pulled out.
''The occasion got to them a little bit. There was excitement which turned into nerves."
New Zealand play hosts Scotland in their second pool game on Saturday.