If your main concern is not wanting to mess up your web design with bylines attached to every graphic, be aware that you generally have some flexibility with how you give attribution. In particular, you may be able to give attribution in HTML comments that don't actually show up on the page.
The full legal text of the international version of CC-BY-3.0 includes this description of the "BY" requirement (emphasis added):
If you distribute, publicly display, publicly perform, or publicly digitally perform the Work or any Derivative Works or Collective Works, You must keep intact all copyright notices for the Work and give the Original Author credit reasonable to the medium or means You are utilizing by conveying the name (or pseudonym if applicable) of the Original Author if supplied; the title of the Work if supplied; to the extent reasonably practicable, the Uniform Resource Identifier, if any, that Licensor specifies to be associated with the Work, unless such URI does not refer to the copyright notice or licensing information for the Work; and in the case of a Derivative Work, a credit identifying the use of the Work in the Derivative Work (e.g., "French translation of the Work by Original Author," or "Screenplay based on original Work by Original Author"). Such credit may be implemented in any reasonable manner; provided, however, that in the case of a Derivative Work or Collective Work, at a minimum such credit will appear where any other comparable authorship credit appears and in a manner at least as prominent as such other comparable authorship credit.
The credit attribution has to be "reasonable" for the medium, but must be included in any comparable credits. In other words, if you have a footer or similar element on the webpage where you or your company as web designers are credited, then you should probably include credit for the graphics there:
Site design by Nifty-Doodle WebPages, with graphics from Cool CC Graphic Source and Other Cool CC Graphic Source.
However, if you don't have any comparable credit on the main page that implies ownership of the graphics, then I don't see anything wrong with putting the attribution in the source code.
However, do make an effort to verify that the images you're using are actually licensed as the site claims. At the very least, consider how much of a hassle it would be to re-do your design if the copyright holder issues a take-down request. Or an invoice for royalties.