Christian Glass, 22, died on 11 June 2022, after he was shot by police in Silver Plume, Clear Creek County in Colorado.
He was born in Christchurch but his parents Simon and Sally relocated to Boulder, Colorado, when he was 10.
Former Colorado police officer Andrew Buen was found guilty of reckless endangerment, but the jury could not reach a verdict on the murder charge, nor could they decide whether Buen was guilty of misconduct.
Christian's father, Simon Glass, said the process kept dragging on.
"We felt it was a pretty clear case. We're surprised and disappointed and looking forward to a re-trial or whatever they do next.
"It's been 22 months since Christian was [fatally shot] ... we were told initially it was Christian's fault. The officers [involved] ... were only fired when the district attorney filed charges ... so it's been a very slow process."
Last year, former police officer Kyle Gould pleaded guilty to failing to intervene to stop the unlawful use of force against Glass.
Glass said the Colorado state had made positive changes since his son's death, as part of a settlement deal, to prevent similar tragedies in the future.
Clear Creek County has agreed to establish a dedicated crisis response team in the county by 1 January 2025, and to dedicate a public park to Christian.
In a statement after the verdict on Saturday, his parents also spoke about more training for officers in the state.
Lawyer Siddhartha Rathod, who is representing Glass' parents, said a second trial could happen later this year.
