If you created an armature with a single bone, and after autoweights, your mesh doesn't move with that bone, it's because the autoweights failed. Blender would provide an error message in this case, but it's easy to miss if you're not looking for it. You might check out Heat Weighting: Failed to find solution for one or more bones if you want more information about how to work around this.
However, here, there are a couple of easy things to do, that are just as easy as autoweights, and better.
Manually assign all vertices to that bone. Enter edit mode on your mesh, select all vertices, and look in properties/object data/vertex groups. Blender should have created a vertex group with the same name as your bone (maybe, "Bone".) By default, the "Weight" slider beneath your list of vertex groups is set to 1.0; if not, set it to 1.0. Then click the Assign button immediately above that slider. Now, all of your vertices are assigned fully to this vertex group, and if you still have your armature modifier from parenting with automatic weights, you'll find your bone works properly.
Alternatively-- not additionally!-- you can bone parent your object to your mesh, rather than armature deforming it. This is slightly different, but generally preferable for reasons of performance and for cases where object coordinates are used in materials. In this case, start by deleting the armature modifier that the parent with automatic weights created. Then enter pose mode on your armature and make sure your bone is selected. Now, in the 3D viewport, select your mesh object, shift select your armature, and ctrl p -> bone relative. Now try our your bone, and you'll see that your mesh moves with it just fine.