Not knowing any system specs of your computer as the forum requirements ask for in the headers: Read This First
I will guess you are Windows 10? Regardless much of what Direct X 11 did was opitimize speed. I can understand where you would think what you think, it sees it could be logical that something older had less requirement but it is not true. Especially on hardware designed for DX11, which yours is. If you want more frames it is in games settings you will want to dial down such as anti-aliasing, textures & shadows etc...
Now on Windows 10 DX9 isn't even directly supported, it is supported through the later versions of DX11 and so on. So while you may think it should work that way it doesn't and won't. Try dialing back those settings and if that doesn't meet your needs it may be time to upgrade to something that does.