The premise of your question is incorrect:
I can no longer claim copyright because my image includes an image licensed by someone else (e.g. Adobe Stock), even if they don't require me to give credit.
Wikipedia has this to say about derivative works:
In copyright law, a derivative work is an expressive creation that includes major copyright-protected elements of an original, previously created first work (the underlying work). The derivative work becomes a second, separate work independent in form from the first. The transformation, modification or adaptation of the work must be substantial and bear its author's personality sufficiently to be original and thus protected by copyright. Translations, cinematic adaptations and musical arrangements are common types of derivative works.
It goes on to quote material from the Berne convention and US law. From the former:
Translations, adaptations, arrangements of music and other alterations of a literary or artistic work shall be protected as original works without prejudice to the copyright in the original work.
From the latter:
The copyright in a compilation or derivative work extends only to the material contributed by the author of such work, as distinguished from the preexisting material employed in the work, and does not imply any exclusive right in the preexisting material. The copyright in such work is independent of, and does not affect or enlarge the scope, duration, ownership, or subsistence of, any copyright protection in the preexisting material.
Therefore, the answer to your question
How can I protect the rest of the image - the portion I created?
By copyright. You don't need to disclaim copyright in the source material of your derivative work explicitly; you don't have that right anyway, regardless of what you say. On the other hand, you certainly can disclaim it. It is common to reproduce the copyright notice of source material, however.
The specific requirement will depend on the terms of the license under which you are using the source material; in your example this would be the Adobe Stock license (pdf), which says
4.1 General restrictions. You must not:
(g) remove, obscure or alter any proprietary notices associated with the Works
If the work is subject to "editorial use only" then there are additional restrictions.
