The problem word here is "dark". Since flash has to be turned off, in a normal camera there are three ways (and a combination of these three) to handle this:
1. increase ISO;
2. decrease shutter speed;
3. decrease aperture value (increase aperture opening).
However, if you're referring to a Windows Phone (or most of the other phones), it would have a fixed aperture - that crosses #3 out.
You can try #1, but you can only go so high until your photos start becoming noisy or grainy*. In addition to this, you could decrease the shutter speed, but that will result in blurry images (especially if you go below 1/125) - the root of your concern.
These are limitations of the device, and nothing else can be done about it in the device except these three.
*- You can try using noise removal software later on, but you will lose some of the details in your image. Or, if your photos are a bit dark (as a result of low ISO and/or faster shutter speed), you may try to adjust their brightness later (using an app or in your PC).