Consider an alternative approach:
Coach: HE DIDN'T FOUL HIM, I DON'T KNOW WHAT YOU WERE LOOKING AT!
You: Coach, I'll be happy to discuss it with you if you can lower your voice.
Crucial first step is to lower the volume. At that point either he will or won't. If he won't, tell him that's enough, then whack him. If he will, then:
Coach: OK, tell me how that was a foul.
You: Well, coach, what did you see?
Coach: I didn't see a foul!!
You: Sure, but what DID you see?
Here, you invite the coach to have his say, which is (or should be) what he's really after anyway. It also gives you a moment to collect your thoughts and review the play in your mind. Again, either he'll take advantage of this opportunity, or not. If not, then move along with the game. If so, then:
Coach: My guy was straight up and down.
You: OK, from my angle he brought his arms down into the shooter, then lifted them back up again.
At this point, you've both had your say. Time to close it down and move along.
Coach: He did not!/That's not what happened!/No way!
You: Coach if it happened your way then I missed it. Now we're going to get back to the game.
Following an approach like this allows you to remain respectful, gives the coach his say, but moves the game along at a reasonable pace. If it breaks down, warn in an even tone, "that's enough" (never: "not another word!" which almost always backfires). Then whack. If he gets personal, whack immediately.
Remember, you've brought a gun to a knife fight.
