What makes you think so?
Please have a look at the formal definition of regular expressions at https://en.wikipedia.org/wiki/Regular_expression#Formal_defi... on Wikipedia, and let me know where the stack and the iterations are. I can't find them.
https://en.wikipedia.org/wiki/Recursive_definition#Well_form... is also a good example.
Regular expressions are a particularly interesting example because you brought up 'loops', so I'm assuming you are interested in how you can implement some of these recursive definitions on a computer.
So for regular expressions a common technique is to compile them to a finite state machine. You can model that in your computer as one block of eg assembly instruction per machine state. To move to a different state, you just 'jmp' to the corresponding code's address.
That's pretty fun to work out, but I still don't see anything I would describe as a 'loop' here; but the recursive analysis still makes perfect sense.
Yes, some programming languages have special purpose looping constructs. But they are of limited usefulness, and not particularly fundamental: they usually get compiled away.
