1) Create a Levels Layer out of the area that is to be burnt in:
* Use the Lasso or Marquee Tool to select the area. Make sure the Feather is set to be large enough.
* Select Inverse.
* Layer / New Adjustment Layer / Levels, Mode: Normal, Opacity: 100%.
2) Burn in the area:
* In the Layer Content Options, slide the Highlight Output Level Slider toward 0.
* Adjust till the desired effect is achieved.