You can use post process, but you really should adjust the lighting as a first reaction rather than trying to tweak with post.
It could also be bounce lighting washing out your scene if its statically lit. Try going into world properties under lightmass and set diffuse boost to 0. Then also set your skylight to 0 and then you should have absolutely black shadows after you rebuild lighting. Then you can slowly enable the bounce and ambient light to your taste (rebuilding after each change).
I would highly suggest you take this route before just messing with post processing since once your post process gets too far away from center it will end up causing issues with everything else you create in the future and you may be really limiting your content range. This can bring out bad precision artifacts etc.