Then again, the reverse isn't true. There are languages (or more precisely their implementations) that just are slow.
Furthermore, good asymptotic complexity doesn't always correlate with faster code for values of n you actually encounter. Linear search is much faster than binary search, because of cache behavior, up to a surprisingly large n on many architectures.
I have had a few experiences of simply porting something rather directly to C++ and seeing 10X speed and memory improvements. The 'hidden costs' in other languages are loads of unavoidable heap allocations and pointer indirection that really don't happen with C++. And C++ compilers do a ton of very smart optimization these days.
With the generic programming constructs and static polymorphism approaches in C++ you can often get really big performance increases over what's practical in C or Java. std::sort in C++, for example, has often been found a few times faster than stdlib.h qsort. It's because of compile time optimizations that languages like C and Java can't do.