The Rama m'Pana famously suggests that the bracha on man was "hamotzi lechem min hashamayim", implying that the man was a type of bread. The gemara (Brachos 48) writes that Moshe Rabeinu composed the first bracha of birchas hamazon, again suggesting that the man required bentching even though it was not made from the 5 species of wheat. Perhaps, as R' Yosef Engel suggests in his Gilyonei HaShas (Brachos 48), if the person eating man thought of bread the man not only tasted like bread but in essence assumed the quality of being bread.
Others sources disagree. The Jewish people complained that "nafsheinu y'veisha ein ko, bilti el haman eineynu" (BaMindab 11). What does it mean to have a "dried up soul" thanks to the man? The Zohar asks why the fasting of Yom Kippur is described as "inuy nefesh", an affliction of the soul -- does the soul suffer because the body is deprived of food? The Zohar amazingly answers that the soul does suffer because it is deprived of the opportunity to make brachos. Here too, it was because the man required no bracha that the Jewish people complained that it endangered their souls. (Cited in a footnote to the Tiferes Yosef.)