Hi Adwul62,
You are not quite correct to say that screenshots do not have a color setting. I just took a screenshot with my copy of Snagit and opened it up in PS and looked at the color settings [Edit (menu) -> Color Settings] and it shows as I would have expected sRGB (the generic "safe" color space).

There is another issue though that I think may be happening: Is the image that you placed into the PDF decreased in original size? That is, did you place the image, and then decreased the X:Y size of the image by dragging the image smaller?
In the image below I took a screenshot of one image and placed it into a PDF and decreased the size of that image a lot. Then I took the same image and place it into the same document and left it large. You can see how the smaller one has a bit of a darker character.
If you did, that explains the problem: when an image in decreased in size, the parent application calculates what pixels to keep and what pixels to toss and it does this by averaging out the general contrast of the image. Below I took an image and placed it large and small in the same PDF. As you can see, the smaller one is a tad darker than the larger one although they are the same image.
Now keep in mind that Snagit automatically assigns a resolution of 72 ppi for any screen grab. That means that if your document is set to (say) 300 ppi and you place a screenshot (at 72 ppi) into the image you will have to increase the size of the image and (here) Acrobat will have to invent pixels to make up the difference. In addition it will appear "soft."
You can see that softness in a close up of the metal leg at the seam at the very top of the leg. The image on the left is soft whereas the same seem is a tad sharper on the right (from your comparison shot).

Whenever possible, try to use an original photograph to place into a PDF rather than a screenshot of a photograph as you did here.
I hope this is your issue, I do believe it is. Please let us know.