"While Danny was offered the opportunity to reapply for the position, we respect his decision not to put himself forward and wish him the best of luck with whatever he chooses to do next.
"The plan now for New Zealand Football is to announce a new All Whites head coach as soon as possible once the recruitment process has been completed."
Hay said he was proud of his time as coach and thanked players and staff.
"It has been an absolute pleasure being at the helm of the All Whites over the past three years and I want to sincerely thank the players and the staff for their unwavering commitment to the team during that time.
"Being a part of the development and implementation of a cultural progress for the All Whites that allows players and staff to connect deeply back to Aotearoa New Zealand, and each other, is something that I'm incredibly proud of.
"That connection piece, along with the courage to play a style of football that represents us as New Zealanders, will hopefully stand the team in good stead as they move toward the 2026 World Cup.
"This exciting group of players showed the world at the Tokyo Olympics, and in the intercontinental playoff against Costa Rica, a glimpse of what the future holds. It is very bright.
"I know they will do the country proud and wish them all well in their future endeavours."
Following recommendations from the de-brief, the recruitment process for the next All Whites head coach will involve representatives from the playing group, the PFA, the NZF board, and the NZF High Performance and Player Welfare Committee, to ensure the best fit possible is identified.
The de-brief, conducted through face-to-face interviews with more than 40 people involved in the qualifying campaign (including more than two thirds of the playing group), was undertaken to help establish what went well and what could be improved ahead of the next World Cup cycle.
While the de-brief found the team was as well prepared as possible for the Fifa World Cup 2022 qualifying campaign, there were a number of recommendations that needed to be addressed ahead of future activity.
"A key priority for NZF is making sure we plan and resource sufficiently for the next four years, giving the All Whites the best possible chance of success at the FIFA World Cup in 2026 and in our 2024 Olympic campaign," said Pragnell.
"One area the campaign de-brief highlighted was the lack of alignment between the All Whites staff and New Zealand Football's high performance department - so that will be a major focus.
"It's critical the All Whites are fully integrated with the organisation if they're to produce the best possible results on the international stage."
Pragnell reiterated New Zealand Football's commitment towards the All Whites, confirming they would play in every possible window after this year's Fifa World Cup, giving them much more time together than the previous Covid-19 disrupted cycle to continue their development.
