Don't give up hope. I once left my carry-on bag on a cart in the downtown Los Angeles train station late at night after an overnight trip from Seattle. I made it all the way out to Long Beach before I realized I'd left it behind. I had noticed a number of shady-looking people hanging around the station, and had no hope of ever seeing it again. BUT -- I prayed to St. Anthony and when I called the station's lost and found the next morning, they said it had been turned in, with everything intact. I think your hat will turn up (or you'll find something even better).
It could be worse--my former housemate went to Alaska with her BF and lost her camera, a large geode she'd bought, a jacket I'd loaned her, her wallet, some gifts she'd bought, and a pair of shoes. These were all separate incidents. I thought that was pretty epic for one trip!
She liked Alaska, but was really bummed out she didn't get pictures or souvenirs.