As an expert in this kind of thing, having spent a lifetime wondering what management are thinking, it could make sense for Martinez to offer his resignation now. It would be his way to show the club how much this all means to him - How he is more upset than anyone. A gesture that answers the criticism that he is ploughing on regardless with no ability to change - This is his attempt to take stock and say "It has gone a bit wrong, and if you think it is just because of me, then I am happy to step down - or give me the chance to win you the Cup and we talk about it later"
Martinez would also feel safe as the club are probably not ready to line up a replacement so quickly - and have actually only just got their heads around the idea of changing managers - So, it was pretty much guaranteed that they would refuse.
Also Martinez would gamble on Moshiri feeling he would have nothing to gain from accepting a resignation now - unless a new manager was already lined up - as if the semi is lost after accepting a resignation, then it would no longer be Martinez fault.