I can't tell you how many times I've heard people use the excuse that their equipment is what's holding them back from being truly great. If you aren't a good photographer with an entry level camera, you won't be a good photographer with an expensive camera. I've seen amazing night landscapes done with a Canon Rebel. I've seen incredible shots created with an iPhone. In my opinion, learning on a camera with limitations forces you to use your creativity and not relay on the camera to cover your butt. You'll have to learn how to properly expose and compensate for the limitations of your camera. Remember, digital is still fairly new. Photographers have been creating compelling photographs long before digital advanced to where it has.
If you're comparing your images to others, stop immediately. Do not ever compare. Study. Study what makes those images great. Is it the depth of field? Is the the expression in the subject? Is is the lighting? Chances are it's not "it was shot with a great camera". If what draws you to the image is the lighting, study how to achieve that lighting. Don't hang your head because you haven't already achieved it.
All cameras and lenses have their limitations. You won't get a super blurry background in your portraits if you don't have a long lens with wide aperture. Instead of throwing in the towel because you can't achieve that look, learn how to make portraits without it. It's possible, even if all you have is a cheap kit lens. Would I recommend advertising yourself as a portrait photographer if that's all you have? Absolutely not. However, that doesn't mean you can't use it to learn and get better. Once you've learned how to consistently create amazing images with what you have, then you can consider upgrading. I learned photography on a Canon Rebel 35mm camera. I had a lot of terrible images that were produced with that, but I also had some that I really liked.
Here are a few photos from before I had my "super fancy camera" and nice lenses. These were taken with an SLR or DSLR with basic kit lenses.