I think it's pretty unlikely that you did any serious damage to the device. The uterus is a fairly muscular organ that cramps on a regular basis, and IUDs aren't damaged by that. You did take a hard fall, though, so maybe it would be a good idea to check with your doctor. He/she can do an ultrasound to make sure everything looks ok in there.
It's more likely that the IUD or the strings shifted enough to cause some abrasion that led to the spotting. If I do a difficult bike workout close to the start of my period (when the cervix tends to be low and open), the string of my IUD rubs on my cervix which hurts like crazy and causes minor spotting.