Intel® HD Graphics 3000 is able to support DirectX* 10.1.
You can install DirectX* 11 manually in a system and still use a hardware compatible with DirectX* 10.1 as this video controller and the system will still operate as 10.1 complaint system (no need to rollback).
One thing you may take under consideration would be installing a new processor with Intel® HD Graphics 4000 that uses the same socket type (LGA1155) after checking for compatibility with your motherboard manufacturer. That way you may get a system with DirectX* 11 and take advantage of the video capabilities that Intel® HD Graphics video controllers will give you such as Intel(R) Quick sync Video 2.0, Intel(R) inTru 3D techonology, Intel(R) Clear video.
For a list of newer processors featuring Intel® HD Graphics 4000 and the LGA1155 socket (the same of the current processor you have), you can refer to this URL: