On Monday, Martin accepted the situation is “really difficult” but insists the players “shouldn’t be in a position where they get criticised”.
“The decision shouldn’t fall on the players because it wasn’t a players’ decision – it was a decision by the association, by the board, the executive. People like me, [FAI CEO] David Courell made the decision, not the players,” Martin told RTE Sport.
“The association has been on record saying we don’t want to be playing these games. I don’t want to play the games but for that to impact Irish football, that’s where I would disagree with some of the voices saying we shouldn’t play the game.
“I agree with the vast majority of what people are saying, but the aspect of not playing the game is where we have a difference of opinion.
“I think it’s [best] for Irish football we go and play the game.”
In May, defender Seamus Coleman says a decision to play the games “should not have landed on our [players] toes”, while captain Nathan Collins insisted “we are not going to stand against” any player who opts out of the Israel fixtures.
“It’s a personal choice for the player,” Martin continued.
“We have a fantastic manager and person in Heimir [Hallgrimsson] who will manage that, but at all stages we must mind the player.
“It should be a player-centre world we are in, we are always mindful of the physical environment the player is in and we need to protect them as much as possible.
“It’s going to be very difficult because it does fall on them because they are on the pitch, but I would hope people can see they are following the decision the association took as opposed to putting them at the centre of this.”