In Nikon photography, am I losing quality by choosing the L setting or is it something else?

I have these settings: ISO 100, Fine, and L so after I download them to my computer, I really can't zoom into the picture as I can with my cellphone images for instance.

I suppose it could be attributed to camera shake or cheap lenses and bad focusing and mirror slap but serious I expect more from a 10 megapixil camera

When I print out the picture it looks even worse so I expect the quality of printing has its influence on the end result.

So you made the mistake of buying a dSLR. Your phone is better. Return the camera. You don't need it.

As to your question why you're losing quality, you're not. Picture quality is hugely dependent on the photographer's skill. The camera is only a tool. What you see in the computer is what you really got. Don't blame the camera. It only followed what you told it to do.

Do this

Shoot in RAW and process those images in Lightroom CC

At ISO 100, you should see high resolution results.

This statement is puzzling

"I expect more from a 10 megapixil camera"

The Nikon digital SLR with a 10 mp sensor I used was the Nikon D200, an eleven year old camera. Slightly newer 10 mp sensored Nikon digital SLR cameras were the D60, D40x and D80

Which do you have?

NOTE: Once you pass 100% view of your images, NO matter what camera you use, pixelation will become apparent.

As mentioned, you need to look at your photographic technique first. Unless or until you fully understand the fundamentals of photography, lighting and composition, your images may suffer from your lack of skills, NOT their potiential to take amazing photos.

For many years (2002 to 2006) I was using a 6 mp Nikon D100 to shoot assignments from magazines and news papers. That sensor had the quality necessary for for those publications.

I eventually replaced the D100 with a 10 mp sensored D200, followed two years later by a 12 mp sensored D300 (I still use the D300 for specific assignments) and now a D500, used to shoot sports and other action assignments.

With the right skills, using your 10 mp sensored camera should produce very high quality images

Check your manual that describes the resolution of your images. You should have your camera set for the highest resolution. 3800x2600 pixels or something like it comes to close to 10mp. What size are your shots? It sounds like you are shooting at the lowest resolution.