UV maps on a flat object

My first post here, trying to master some basic Blender skills.
I am trying to create a very basic mesh, it is flat since there is no depth on the z axis, and therefore applying a texture I have already.
I start with loading the texture as background so I can draw a mesh around the edges of the shaoe of the object I am creating then I unwrap and try to apply the same texture as UV map. The problem is that the unwrapping of the mesh changes the things a bit while I d like the unwrapped mesh to be basically the same as the mesh (remember no depth so it should work that way)
any hint?

You can use U / Unwrap from view for the uv to be the same as the 3d view.
By the way, this should have been posted in one of the Support forums, not in News & Discussion.

Unwrap using projection might also be useful for you.

Go to top view, select all vertices click u and click on project from view

Thanks and sorry for the poor choice of forum.