"We are disappointed they will be screening together but we understand the positions of both parties.
"There could have been a bit more thought there."
MediaWorks TV programming chief Kelly Martin said the schedule for Underbelly, which received nearly $4 million in NZ On Air funding, was decided months ago.
She said: "We can't do a lot more to change it without creating a whole lot more drama."
Martin said the fact that two high-quality dramas were screening simultaneously indicated a "coming of age for New Zealand drama".
She added: "I find it works better for us if we focus on what is working for us. [TVNZ] get a bit more wound up about us than we do about them."
She added that the two programmes would appeal to different audiences. Nothing Trivial was aimed at a slightly older "female-skewed" audience, whereas Underbelly, the first NZ-made version of the highly successful Australian franchise, was a true-crime thriller.
Nothing Trivial, which received $6.9m from New Zealand On Air, gained the biggest ratings for a locally made drama since 2000, with an average 516,300 viewers watching the first episode.
A TVNZ spokeswoman said: "TVOne operates in a highly competitive broadcast environment and we are extremely proud of our new local drama Nothing Trivial.
"Our focus has been on its successful launch. It's already been a hit with audiences who have a real affection for it."
NZ On Air's Wrightson said she hoped viewers would still get to see both shows via On Demand or on channels such as TV3 plus One.
Writing in On Film magazine, editor Philip Wakefield said it was unprecedented for two drama series with such high profiles to clash.
"Whatever one might think of their creative credentials, both boast first-rate production values and their primetime face-off should be celebrated for having achieved a level of excellence to where they're worthy adversaries," he wrote.