This is now your second thread on basically the same subject, and despite the fact that I replied to you with some help in the other thread, you gave, no response, no update on if it worked or didn’t work, and no thank you.
Despite my better judgement, I’ll reply to this one.
UNITY needs an actual UV map, not just interpreting one. The “generated projection” you used in Blender will NOT transfer to Unity, in fact this is true of “every” 3D program because it’s NOT creating a UV map, it’s just generating one on the “fly” to make it render. While it may not be convenient and you may not “like” the answer, you need to unwrap the model and make an actual UV coordinate map for Unity to be able to apply your texture to the model.
Next, your texture is non-square. This is, generally speaking, not a good thing. Typically what you do is unwrap the model into a square grid with a “blank” texture of whatever pixel size you want (256x256, 512x512, etc), and then paint the colors you want in various places in Blender using the paint tools, or export the grid to photoshop/GIMP, paint the texture over the UV grid, then import into Blender. You can even use your current texture as a sample set for painting the new texture.
If you’re dead set on using non square UV’s, then I would probably do the gradient texture the “other” direction (left to right instead of top to bottom), and just UV map the bowl in half, so one half is on one side of the texture and the other half is on the other side. This will have some overlap of inside and outside, but that seems to be what you’re trying to achieve, bottom brown, top edge black anyway. I have no idea how well Unity will deal with non square textures though…so the point may be moot, and I’ve never tried it myself.
To unwrap and split the bowl in half, go into edit mode, enter edge select mode, hold down ALT and click on an edge loop that passes all the way through the middle of the model, you may need multiple edge clicks with SHIFT to get it to go all the way through the model, depending on how your edges are aligned. Hit CTRL+E and choose Mark Seam. Open the UV editor, add a blank texture of whatever size, hit U to unwrap. Now either paint the map in blender, or go to the UV’s menu, choose export UV Layout, chose your format of choice, open the image in whatever paint program and make the texture map to the UV’s. You’ll need to cover up the edge grid completely or it will map back onto the surface in Blender when you import it back in.
Lastly, the .blend file import doesn’t “just” work with 2.49, it also works with 2.5x, but you need to download an update to the import/export python file here on the Unity site in the forums somewhere, do a forum search. Of course I haven’t tested this in Unity 3.4 yet…because, well, it just came out yesterday. 
You can also view a video tutorial here if what I said above didn’t make sense:
http://www.blendercookie.com/2011/01/21/intro_uvmapping/
