If the booking was successfully canceled then you would have received a cancellation email. If you have that, it's an open and shut case. If you did not receive a cancellation email then you are probably going to have a tough time convincing JetBlue otherwise.

I will say that I've made (and canceled) hundreds of JetBlue reservations over the years and never had the issue you mentioned. Not sure what glitched when you tried to cancel but it seems like an outlier.