Well, the Mana series is loosely/technically part of the FF series (The first game of the series IS Final Fantasy Adventure), moogles and all.

As for your question OP, (being vague for spoilers) the dungeon in Rak'Tika- there is a part where you jump down a waterfall. In front of you is a huge tree, complete with pink birds flying from right to left. If this isn't a nod to Secret of Mana's opening title screen, I don't know what is.