What you're missing is a lot of scene coverage. To get a 360ºx180º full spherical view, you have to cover the entire sphere. Without a fisheye lens, this is likely to mean multiple rows as well as a zenith and nadir shot, with precise coverage.

In hardware terms, this probably means you need a panohead on a tripod--or at least a plumbline--to make sure you rotate somewhere close to your lens/body's no-parallax point in space, both in pitch and a yaw.

Fisheyes are most typically used because they can easily yield more than 130º of HFoV (horizontal field of view--coverage across the long edge of the frame). A rectilinear lens has a lot smaller coverage. So, for example, if you're using an 18-55 kit lens, zoomed out to 18mm, the coverage you can get on an APS-C body is typically HFoV: 64º; VFoV of 45.2º (see Bob Atkins's FoV calculator).

So, if you hold the camera in portrait orientation, to cover the 360º in yaw, you'd need: 360/45.2 => 8 images around in yaw, and to cover 180º in pitch (from straight up to straight down), you'd need 180º/64 => 3 rows for each of those 8 images. And that's without any overlap, which you require for stitching. If you assume 25% overlap, then that's more like 3 rows of 10 images each plus a zenith (straight up) and nadir (straight down) shot.

So you can see why having a panohead with marked detent stops every 30º or 45º or so to track coverage, or a much wider lens might be a good thing for this type of shooting. Conversely, shooting with a rectilinear lens does get you a much higher-resolution final panorama, so there is a plus side to having to do all the additional stitching.

See also:

• What are the best techniques to take 360° panoramas?
• How are virtual tour photos taken?