What's the best way to use regex in searching for files named via some pattern in linux?

What's the best way to use regex in searching for files named via some
pattern in linux?

I have file names that are named thusly...
[phone_number]_[email]_[milliseconds].mp4
so:
2125551212_foo@blah.com_1378447385902.mp4
find takes a regex pattern (supposedly) to look for files that start with
10 digits and end with mp4like this:
find ../media_pool -regex '^\d{10}.*mp4$'
However that returns nothing at all.
When I try it thusly: find ../media_pool -regex 'mp4$' it returns all the
files that end with that extension... so, it *looks like it works with
some subset of regex but not all.
Can someone point me to what the right way to get what I need would be?
I'm happy not to use find if something else does the job better.