You're pretty much correct. True regular expressions don't have the expressive power to decide whether arbitrary-length strings are or aren't palindromes.
That said, 'regular expressions', as used in most programming languages, have extensions that extend the expressive power. One such extension is the matched group & backreference, used in other commentor's answers.
From a theoretic stance, these aren't really 'regular expressions', but that's what we call them in practice.
