You either admit the mistake and go with inadvertent whistle, or you enforce whatever you call in which case you're not admitting a mistake - you could later admit you
may have kicked it.
If you whistle for an illegal dribble, for example, and then determine you shouldn't have, then just take the blame right then and go with IW. If it's a close judgement call with a quick whistle on a foul or a violation that isn't 100% clear to you - you're probably better to make the call, get the ball back in play, and get on with it. Later, if the coach questions you, explain what you saw and say, "Coach, you may be right and I may have blown that one." You can use that one very rarely and you're usually okay.
If you realize you've made a mistake and are certain you shouldn't have blown the whistle, it's always appropriate to go IW. Kick yourself in the shorts mentally and then get back to officiating the game. And don't let it happen again. Ever.
