Fun Fact: The title of the game was inspired by designer Hironobu Sakaguchi's thoughts that if the game was not a success, he would have to quit the industry.
The Dragon Warrior series opened the door for RPGs on the NES, and Final Fantasy walked through it. It's not unreasonable to give Final Fantasy the credit for popularizing in America what would become known as the JRPG genre, as it gave birth to a game franchise that would continue to be a major industry force two decades later.
Final Fantasy adopted the basic design mechanics that the Dragon Warrior series pioneered, like a top-down overworld map for navigation, menu-based combat (but without the first person view), character classes and operating within a party structure. What Final Fantasy brought to the table, and why it was held in such high regard, was a better story in the eyes of many critics. Final Fantasy also caught flak for being just a clone of the Dragon Warrior series.