Chain of command me lad, chain of command. I dunno how it'd be in the US, but in Australia it'd be:
"Bugger.... Corporal, I lost my bloody ID tags, can you hook us a new set"
The corporal will have his words to you, he'll then put things in progress to get you a new set through the platoon commander. It costs nothing, you don't really get in any trouble, and you keep your integrity. They prefer it if your honest with them, rather than lie or try to hide things from them.