Was there a specific reason why garbage collection was not designed for C?

Garbage Collection is not useful if you want to make hardcore optimisations, because if you decide the moment when it's best to free allocated space, then you can make a much better job in your project than the garbage collector does. In the 1970s I don't know the exact cause why the developers decided to not include a garbage collector to C, probably they wanted to have absolute control of deallocation, however I'm sure later they didn't even consider to add a garbage collector, because even if there is an integration of a garbage collector to the language which is very good, there were built a lot of C projects and the new versions of the language must have backwards compatibility.

EDIT: "There are also compilers, libraries and operating system level mechanisms for performing array bounds checking, buffer overflow detection, serialization and automatic garbage collection, that are not a standard part of C." This may be interesting for you, you can read more here.