Short answer to your original question: no. Longer answer: you're creating a derivative work. Just don't claim authorship of all the components of your work. I would liken it to quoting other people's work in an article or book. Acknowledge your sources and you're fine; claim them as your own words or the results of your own research rather than theirs and you're plagiarizing.
I'm neither a lawyer nor a legal scholar. The way I think it works is that you can claim copyright to the derived work, which is your creation from the copyright-protected work of others. A song that uses a sample from another song deserves protection, and so does your derived work. It still depends on honoring the copyrights of its components.