Lynn, if your experience is like mine, yes you will have problems going forward. And I'm sorry for your loss. I used to let my cats out and never had any pests in my yard. No gophers, moles, shrews or rabbits. I stopped letting the cats out several years ago because one got killed by a car, and there was a neighbor cat around who had feline leukemia. Then some passers-by tried to take one of them. So I won't go back to letting them out, but I surely miss their pest control services!
Cinta, I plan to try the glass/gravel deterrents in the spring. The ground is too frozen now to dig.