The GPL is a copyright license. Its restrictions are a subset of those imposed by copyright law.
In very broad terms, copyright protects copying, distribution, modification, and various similar rights such as "public performance or display" (usually for artistic works). So, if you never distribute, modify, or copy* GPL'd code or binaries, then the GPL does not apply to you and it does not matter whether someone, downstream of you, does one or more of those things. However, that hypothetical person might have difficulty complying with both your license and the GPL, and might therefore choose not to distribute your software at all. Whether you consider that a problem is your decision, of course.
The position of the Free Software Foundation, and most other people in the open source and free software communities, is that APIs cannot be copyrighted. Numerous people have said as much during the Oracle v. Google lawsuit. If this is in fact legally correct, then "using an API" also does not require a license. If this is legally incorrect (in your jurisdiction), then you may need a license from whoever developed the API in the first place, which complicates this analysis somewhat. However, I would certainly hope and expect that most reasonable authors would be willing to place their APIs under permissive terms or a CC0 public domain dedication. Unfortunately, this is a relatively new problem, and most existing licenses do not take it into account.
* In general, most if not all of the GPL's obligations attach at time of distribution. Making private copies or modifications does not usually trigger any obligations by itself. This is not true of, for example, the AGPL, for which section 13 attaches at time of modification.