You did the right thing. You reported it to the staff. It's their job to deal with it.
Don't confront a shoplifter. My DH was a retail manager for most of his working life. He used to have to detain shoplifters and, when he was younger, he used to sprint after them and catch them if they ran for it. One of the men he caught punched him in the face, and he ended up with a massive black eye. His Area Manager thought it was funny but I didn't. It could easily have been a knife instead of a punch. He also had to ban a group of teenage girls from the shop as they were persistant thieves, and for several nights they waited for him in the underground car park. One of them was armed with a baseball bat. I was frightened for him but luckily there was a security man in the mall, and he would accompany my DH to the car after the first incident. There was another group of shoplifters, young men this time, who found out where his car was parked. In revenge for being banned, they jumped on the car's bonnet and stove it in.
The point I'm making is that you don't know what you're dealing with. Thieves can turn nasty and you don't want to be on the receiving end. Shops don't want you to get involved and get hurt. That's worse for them than the shoplifting. All you can do is report it.
At the shops where my DH worked, the policy was always that the staff had to witness the theft themselves, and couldn't rely just on customer information in case they were mistaken. If a customer reported that someone was stealing, my DH or a shop assistant, or both, would covertly watch the suspect until they caught them in the act. If the thief didn't steal anything else or it was reported after they left the shop, they couldn't do anything.
That was the policy in theory,anyway. I think that, on a few occasions, my DH might have taken a chance and challenged the thief if there were several customers who had witnessed the theft. Whatever the shop staff decided to do, you have done all that you could by reporting it.