The Torah states that after Bnai Yisrael cried out to Hashem when they saw the Egyptians pursuing them, Hashem said to Moshe, "מה תצעק אלי," "why are you crying out to me" (שמות י"ד:ט"ו). Many Meforshim ask why Hashem said this to Moshe, because it seems that Moshe didn't cry out to Hashem at all. Moshe didn't say anything to Hashem. Apparently, Moshe must've said something, though, but the Torah doesn't mention it. The Torah simply records Hashem's reply to Moshe, "דבר אל בני ישראל ויסעו," "tell Bnai Yisrael to move" (שם). What exactly is going on here?
Ibn Ezra says that Moshe represented all of Bnai Yisrael that were crying out and complaining against Hashem, asking if there were not enough graves in Mitzrayim so that they had to be brought out to die in the desert (שם פסוק י"א). In other words, Moshe indeed said nothing to Hashem, but Bnai Yisrael did, as an earlier Posuk says (שם פסוק י'), but Moshe was spoken to by Hashem as the representative of Bnai Yisrael. The Ramban, however, refutes this explanation, because if Hashem was really addressing Bnai Yisrael, He wouldn't have said "why are you crying out," because they had a right to cry out when they saw that they were being pursued. He then says that perhaps Ibn Ezra means that Hashem was asking Moshe why he let them cry out, because he knew Hashem would save them, but that isn't what the Posuk says, it says מה תצעק, why are you crying out, not why do you let them cry out.
The Ramban therefore says that it was indeed Moshe who was Davening and crying out to Hashem. Although Hashem had told Moshe that He would take care of Paroh and his men (שם פסוק ד'), Moshe still didn't know what to do at that moment when they were at the edge of the Yam Suf and the Egyptians were chasing after them. This hesitation on Moshe's part is consistent with his character. We know that Moshe ultimately took Bnai Yisrael out of Mitzrayim, but he was initially very hesitant to do so; he kept saying he couldn't do it and that he wasn't the right person for the job, and so on. Perhaps we see the same kind of hesitation here.
The question still may be asked, however, as to why it was necessary to leave out Moshe's Tefillah here. If, as the Ramban says, Hashem was so upset when Moshe cried out to Him by himself, why not tell us just what Moshe said? One could answer this by saying that the Torah actually did tell us Moshe' rayer, and we may derive it by examining Hashem's response. When Bnai Yisrael say to Moshe that He shouldn't have taken them out of Mitzrayim because they would rather still be slaves there than die the desert (שם פסוק י"ב), Moshe answers them by telling them not to be afraid, but to observe the might of Hashem, became He will fight for them, and they should just be quiet (שם פסוקים י"ג-י"ד). Perhaps this was Moshe's unknown Tefillah. He tried to reassure Bnai Yisrael, but was really asking Hashem what to do, and how to take care of the people's complaints. To this, Hashem says to Moshe,"מה תצעק אלי דבר אל בני ישראל ויסעו," "why are you crying out to me; tell Bnai Yisrael to move (שם פסוק ט"ו). Hashem says to Moshe, "Why are you trying to answer the complaints of Bnai Yisrael, which have no substance or purpose." "Whenever things look bad for them, they just complain, so don't try to answer them." "Just tell them to move," "דבר אל בני ישראל ויסעו."