You need to set inner glow (yes glow not shadow) in your object. Set your desired color, blend mode and size (as in your image it could be black color and multiply)
How to set inner glow? Right click on layer with your object > Choose Blending options > Check and set Inner Glow.
Then you can easily apply this effect to other objects by copying layer style. Again right click on object with layer style > copy layer style > paste it to another object(s).