First thing is, one should go and research further into the details of copyrights as they relate to images. It provides more detailed explanation concerning these matters, and in more legal description discerning acceptable, non-acceptable, and the 'grey areas'.
Second thing is to get a sense of any TOS, or Rules, associated with the Party/Site/Company (whichever) that you are attempting to display your artistic creations through. They tend to generate not just their own rules to assure no copyright violations are occurring, following the guidelines based on regulations, but may also be having to follow those of some type of sponsor. These sponsors can be any type from Advertising to Payment/eCommerce companies which enforce their own policies. I know of one site that subjects it's members to this and what is or is not allowed of content, due to the company they use for Financial Transactions via the website.
As far as just the nature of the design itself. It can have a lot to do with if it is held within a current copyright. A LOT of times, images are 'chopped'- taking an image and using software like Photoshop to cut/paste/redesign/change/incorporate, etc. the image into something of their own creation. The problem is, most times this is commonly seen is in works associated with Pop Art. Using works of artists such as DaVinci's Mona Lisa, and making new creations utilizing the image. The thing about these types though are... they hold no real owned copyright, to the artwork itself. Images of the Mona Lisa, created or taken by a company however, are subject to copyright- not of the Mona Lisa, but the IMAGE of the Mona Lisa they made.
If using these images, most times the source must be posted with the image, much like sourcing quotes in journalistic endeavors as to prevent plagiarism.
If the image you created was merely a spoof, then how was it presented... and to what extent was the image being claimed as 100% artistically created by you, and not 'outsourced' image use? I have not seen the image obviously, so it is difficult to tell as to just how much it is an original creation, and a simple 'Photochop' of another's copyright imagery.
Also, it is not understood as to why the image was made for Zazzle. Was this something for mere showcase, some contest, or for some way of profit?
Depends on the image, the artist/intent, the publisher, publisher associates, copyright laws, and so forth.