New Zealand were kicked out of the under-23 tournament this month, after their beaten semi-final opponents Vanuatu successfully protested that South African-born defender Deklan Wynne was ineligible for the Oly-Whites.
The Oceania Football Confederation disciplinary committee last week provided a written explanation for the disqualification.
The reasons will be disputed by NZF following scrutiny from its lawyers.
"Having had the opportunity to review all of the information now available, we remain disappointed at the sequence of events that led to the harsh decision to disqualify our team," Martin said in a statement.
"The executive committee has therefore unanimously agreed that there are sufficient grounds to appeal, both in terms of the process undertaken, and the rules applied. We will be filing our appeal later this week."
Auckland-based Wynne, 20, holds a New Zealand passport and has played three senior internationals for the All Whites.
The OFC cited football governing body FIFA statutes which say a player must have resided in a country for five years after the age of 18 if he doesn't have parental or grandparental bloodlines.
Martin confirmed an internal review was under way at NZF to ensure the issue of player eligibility doesn't arise again at an international tournament.