It's like when a dog pees on the carpet; you either catch them right away or you have to rub their nose in it before you punish them. Since we're not allowed to rub the coach's noses in anything, we have to punish them right away; thus perhaps this response would be best: "Coach, I didn't hear it, but I would have to assume whatever you said right before the whistle is what got you your T."

Now that would fit in perfectly with my smartazz, sarcastic nature!!! I love that line, and the reaction from the coach would probably earn him/her a free trip out of the gym!!!
OT - My first year on varsity, I had a coach yell at me "You can't call that!!" I said, "Yes I can, I just did" On an unrelated note, soon after that interaction, I issued my first technical foul on the varsity level. Since then I have worked hard on the internal filter:D

I think the technical foul was clearly earned in this case.

You are very right in that as a younger looking official, on most nights, you will be the unknown to the coach. My advice would be to: 1. Get your plays right, 2. Offer professional responses to questions 3. Listen to coaches when they have a genuine concern and are voicing so in a professional manner.

I think if you follow those rules, then you just need to get games so that the coaches see that you can work and develop trust in your abilities.