The Torah attests, "Moses was the most humble person on the face of the earth" (Numbers 12:3). It should be no surprise, then, that the world's humblest person omitted his name from the story, and instead he attributed all the credit to God.
Your question raises an interesting point. After a full year in the desert, the Jewish People celebrated the Pesach festival. They offered the Paschal lamb and ate matza and maror bitter herbs. But when it came time to tell the Pesach story, who did they tell it to? To whom did they relate the plagues and miracles, the Strong Hand and Outstretched Arm? Everybody was there! Everyone saw it with their own eyes!
Only one person had children who did not personally experience the going out of Egypt - Moses! Moses' two sons were in Midian during the Exodus. Moses, therefore, was the first person in history to relate the Pesach story to children who didn't know it first-hand.