I actually don't think you can run Firefox directly from the mounted disk image, but it sounds like that's what you did. Drag & Drop installation from mounted disk images is something that commonly confuses new users (it is in fact a rather confusing installation method). You need to mount the disk image, drag & drop the Firefox icon into your Applications folder, unmount the disk image, then trash the disk image file.
If you think you installed it correctly, you could try Spotlight to find the Firefox application.