Smith is now set to face Rangers in the league on Saturday to continue his comeback ahead of a Hampden rematch seven days later.
When asked if he feared the cup final might have been beyond him, the 33-year-old said: “I had doubts beyond that, I thought maybe I might not even play again.
“It was a frustrating injury. I trained on Friday and went to take my son to a trampoline park. I tried to stand up afterwards but my legs were just in agony. I could hardly walk. My son was like ‘what’s up with you?’ and I said ‘I’m near dead here’.
“I’ve had back problems for about 10 years now and eventually it caught up with me and it gave way.
“I got a scan and one of the discs had exploded into the nerve canal. It was just a mess in there.
“It was close to having to have an operation which would have kept me out for longer. Thankfully, I recovered well.”
Smith added: “It’s been tough. It was a weird injury because I couldn’t do anything about it in the gym, it was just about trying to recover.
“I finally got the green light from the specialist to start playing again so that was nice. I can now look forward to the final.”