Not sure how well you know Photoshop but a quick summary of the easiest way is:
Layer 1: Create the background of the document by applying the colour you want - in this case colour #136652
Layer 2: Drag or copy/paste your logo
Layer 3: Add any element not to be affected by the logo - i.e. Images of people/text etc.
Then go back to layer 2 and adjust the layer mode in the drop down box and then play with the layer opacity. For example 'Luminosity' at about 8% looks reasonably close but if you use this mode you will also need to use the magic wand to select the white areas of the logo image and cut/mask them.
In Photoshop there's a thousand ways to skin a cat but play with these layer modes for a pretty simple way to achieve what you want.