Firstly, that Wynne - and every other member of the New Zealand squad - was ruled eligible by the Pacific Games Council, after the team paperwork was submitted ahead of the tournament.
Martin said there was "much uncertainty" in the buildup to the event, with the OFC Olympic qualifying event held within the framework of the Pacific Games. But he said the rules were provided in advance, there were individual declarations on eligibility and NZF "acted in good faith at all times."
The second point is around a legal interpretation of Fifa's statutes governing eligibility, as they are not black and white. OFC have applied article 7 of the Fifa regulations governing the application of the statutes.
"We have all gone to what was quoted and the fact that we can't say - hand on heart - that it is crystal clear is a real problem," said Martin, of the relevant Fifa statutes.
"The right thing to do is get the lawyers to look at it, to test the thinking and we will stick by what they say."
Martin added that no one at NZF "has gone out of the way to mislead, to cheat..the system."
NZF has until the 27th July to lodge their appeal with the OFC Appeals committee.
Martin said the organisation believed all players were eligible and had received confirmation of this from the organisers of the Pacific Games, of which the qualifying tournament was a part.
"We acted in good faith throughout," he said.
"Deklan is the innocent party here and we ask that his privacy is respected."
Martin said he would have expected any issues with ineligibility to have been raised with New Zealand Football before such a decision was made.
Earlier, a despondent New Zealand Under-23 football side landed at Auckland Airport after being disqualified from their Olympic qualifying tournament in Papua New Guinea.
The Oly Whites had beaten Vanuatu in the semifinal and were just hours from taking on Fiji in the final when they were ruled to have played an ineligible player, South African-born defender Deklan Wynne.
Coach Anthony Hudson said at the airport that the team had received news of the disqualification "bit by bit", with the final decision leaving them all in shock.
Steven Holloway: How did it come to this?
"If you'd have asked me 24 hours ago, I would have been really saddened and disappointed. But as a coach ... when it's out of your control you have got to move on and pick the players up and this will prove to be a really huge moment for us."
Vanuatu took New Zealand's place in the final on Sunday night, going down 4-3 on penalties. Fiji's victory put them on the path to the Rio de Janeiro Olympics.
Hudson would not answer any questions about the ineligibility ruling for legal reasons, but said at one point that he did believe everyone was eligible to play.
Wynne was deemed to have failed to meet the Fifa regulations for a player born outside the country he was representing. According to Fifa, there are four criteria that qualify a player to represent a country if he assumes its nationality.
He must have the passport of that country plus meet one of the following requirements: Be born in the country, have a parent born in the country, have a grandparent born in the country, or have lived continuously in the country for five years after the age of 18.
Wynne, who is aged 20, holds a New Zealand passport, but does not meet any of the four criteria.
He moved to this country from South Africa in January 2010.
When asked early today if he knew he was ineligible, Wynne replied, "I had no clue."
He said he was "really disappointed", but he knew he had the backing of the team and New Zealand Football.
He said they all had his best interests at heart, and he trusted them.
"I love playing for New Zealand and I want to keep playing for New Zealand in the future."
Wynne said he didn't know what the ruling meant in terms of playing for his country in the future.
