I'm making a tile based game in XNA

So currently my lightning looks like this:

How can I get it to look like this?

Instead of each block having its own tint, it has a smooth overlay.

I'm assuming some sort of shader, and to tell it the lighting and blur it some how. But im not an expert with shaders.

My current lighting calculates the light, and then passes it to a spritebatch and draws with a color parameter

EDIT: No longer uses spritebatch tint, I was testing and now pass parameters to set the light values. But still looking for a way to smooth it