The real answer is that the only way to make a safe, efficient garbage collection mechanism is to have language-level support for opaque references. (Or, conversely, a lack of language-level support for direct memory manipulation.)
Java and C# can do it because they have special reference types that cannot be manipulated. This gives the runtime the freedom to do things like move allocated objects in memory, which is crucial to a high-performance GC implementation.
For the record, no modern GC implementation uses reference counting, so that is completely a red herring. Modern GCs use generational collection, where new allocations are treated essentially the same way that stack allocations are in a language like C++, and then periodically any newly allocated objects that are still alive are moved to a separate "survivor" space, and an entire generation of objects is deallocated at once.
This approach has pros and cons: the upside is that heap allocations in a language that supports GC are as fast as stack allocations in a language that doesn't support GC, and the downside is that objects that need to perform cleanup before being destroyed either require a separate mechanism (e.g. C#'s
using keyword) or else their cleanup code runs non-deterministically.
Note that one key to a high-performance GC is that there must be language support for a special class of references. C doesn't have this language support and never will; because C++ has operator overloading, it could emulate a GC'd pointer type, although it would have to be done carefully. In fact, when Microsoft invented their dialect of C++ that would run under the CLR (the .NET runtime), they had to invent a new syntax for "C#-style references" (e.g.
Foo^) to distinguish them from "C++-style references" (e.g.
What C++ does have, and what is regularly used by C++ programmers, is smart pointers, which are really just a reference-counting mechanism. I wouldn't consider reference counting to be "true" GC, but it does provide many of the same benefits, at the cost of slower performance than either manual memory management or true GC, but with the advantage of deterministic destruction.
At the end of the day, the answer really boils down to a language design feature. C made one choice, C++ made a choice that enabled it to be backward-compatible with C while still providing alternatives that are good enough for most purposes, and Java and C# made a different choice that is incompatible with C but is also good enough for most purposes. Unfortunately, there is no silver bullet, but being familiar with the different choices out there will help you to pick the correct one for whatever program you're currently trying to build.