Sefer Ohr L'Shomayim explains Moshe Rabenu's tefillah to Hashem by citing the explanation of Sefarim Hakedoshim (Shlah Hakadosh on Parshas Shemos, Torah Ohr) of the Medrash (Shemos Rabbah 23:5) that says: "Tzadikim will say shira in the future." They explain that tzadikim possess a very high level of emunah and, as a result, when they need to daven for a certain thing, they pray in the form of a shira. Their trust in Hashem is so strong that they are certain that He will fulfill their request, so they sing and praise Him as if it has already happened.
This was the level of Moshe. Whenever he prayed, it was in the form of a shira.
The Baal Haturim notes that the word "va'eschonon" has the same gematriah as the word "shira". This indicates that Moshe's tefillah was in the form of a song of praise and thanks to Hashem.
