Unwanted color shift

Would there be a reason why Photoshop appears to be shifting my colors, even after I specify them? I'm prepping photos that were taken of product for our company website. At first, I converted them all to GIFs with transparent backgrounds, but that was starting to create major lagtime in accessing the site. Now I'm trying to convert the originals to JPGs with a background color that matches the website background, but my background colors aren't consistent, and I can't figure out why.
I started by taking the color I was using on the website and used that to paint the background of the photo. When I loaded that JPG on the site, the color did not match the page's background color. I used the eyedropper on the picture and found out the color was no longer the same color I specified (it wasn't an issue of eyeballing it incorrectly,... I had entered in the exact R, G, and B values).
I did some further testing with the "Save for Web" function and various RGB values to see if there was some pattern to the testing. It doesn't appear that colors are being scewed to a value relative to the original color, nor does it appear that the colors are mapping to certain nearby values.
Do I need to check or change any settings in Photoshop so it won't do this? I can provide specific examples, if that'll help people understand.

It's not Photoshop that's changing your colors, it's the compression in the JPG format. I quickly made an image here with a color ramp inside of a single color thick border. We could imagine that this border is the same color of a web page background I'm trying to match. I saved this image as a JPG three times with varying degrees of compression (0%, 50%, & 100% quality settings). As you can see, on each level the precise color of the blue border is different indicating that JPG compression is altering the colors.

You may be suprised to find out that even at 100% quality the JPG format still doesn't get the exact color of blue correct. This is one of the MANY reasons why I despise the JPG format. ... but what can ya do. [shrug]

Have a look at that image here.

You can try using Weighted Optimization to see if that will help particular colors remain unchanged. I once wrote up a brief "how-to" on weighted optimization in Photoshop, you can see it here.