Just like any other product being released, if you're unsure of the compatability of your software with everyone else's computer, you resdistribute the software that is required for your software to work.
To be honest, if DirectX11 didn't work for YOU to run the game, why would it work for someone else to run your game?
You would want to redistribute DirectX10.1 with your game (there is a redistributable version of DirectX that you can pack into the installation of your game)
The one and only,
Only those who sow the seeds of their desires will reap their benefits later.
However, I have seeds of my own to tend to. I don't have time to be someone else's watering can.