I did exactly the same thing. (Only in my case I was sorta innocent. I
extended a circuit that had only one 15a outlet on it, so I naturally
assumed it complied with code and was a 15a circuit. wrong...)

Anyhow, I couldn't see how they could ever use more than 15a on the circuit
and replacing the 14 would be a PITA, so I changed to a 15a breaker.

If you can't do that you will have to upgrade the wire. Sorry.