How do IRL pilots know when they get a kill?

In DCS, you get a little popup that tells you when you get a kill, but it got me thinking, how do real life pilots tell?

Obviously if you're a fighter pilot and you just watched your target turn into a fire ball, they're probably dead, but I'm talking about ground attack pilots. If you're dropping bombs on some tiny tank on the ground, or firing an Anti-radiation missile at some SAM sight way out of visual range, how are pilots meant to know they actually hit it, and that their mission is done?