This is actually a bit of a perpetuated falsehood. While it is true that C programs are frequently faster, this is not always the case, especially if the C programmer isn't very good at it.
One big glaring hole that people tend to forget about is when the program has to block for some sort of IO, such as user input in any GUI program. In these cases, it doesn't really matter what language you use since you are limited by the rate at which data can come in rather than how fast you can process it. In this case, it doesn't matter much if you are using C, Java, C# or even Perl; you just cannot go any faster than the data can come in.
The other major thing is that using garbage collection and not using proper pointers allows the virtual machine to make a number of optimizations not available in other languages. For instance, the JVM is capable of moving objects around on the heap to defragment it. This makes future allocations much faster since the next index can simply be used rather than looking it up in a table. Modern JVMs also don't have to actually deallocate memory; instead, they just move the live objects around when they GC and the spent memory from the dead objects is recovered essentially for free.
This also brings up an interesting point about C and even more so in C++. There is something of a design philosophy of "If you don't need it, you don't pay for it." The problem is that if you do want it, you end up paying through the nose for it. For instance, the vtable implementation in Java tends to be a lot better than C++ implementations, so virtual function calls are a lot faster. On the other hand, you have no choice but to use virtual functions in Java and they still cost something, but in programs that use a lot of virtual functions, the reduced cost adds up.