Unfortunately you only get two weeks to appeal
You can appeal online. Take a picture with your phone, upload it with a two sentence explanation, and the fine goes away. Most parking and traffic citations allow for online appeal these days.
I've noticed that municipalities that have this over-aggressive enforcement also seem to have quite sensible people involved in the appeals process.
You found a ticket on your car, "called them up" and didn't appeal even though you had two weeks to do so? Even if you didn't have a smartphone, you could have walked over to the Santa Cruz public library and done it on one of their computers.
I hate that local governments are so starved for cash that they have to resort to this stuff. It pisses everyone off and it's bad for business. But you could have easily gotten out of it, assuming your story is true and this bothers me. I'm not accusing you, but there are people who would rather have a problem to complain about than a solution.
By the way, the ticket that was place on your car almost certainly has a URL to the website where you appeal online. There are no penalties for appealing (unless you demand a hearing, in which case their might be). I recommend that anyone who gets ANY parking citation appeal it immediately. Don't make it easy for them to get your money, it just encourages them.