Infield Fly if you don't call it immediately

[FUBLUE]

Here's one for the records:

I was working my 6th game of the day this weekend, and in the top of the first it's already 5-0 with bases loaded and one out. Batter hits high pop-up about 15 feet in front of plate, within 5 feet of first base line. I point say (not extremely loud, but loud enough catcher says she heard me) "INFIELD FLY IF FAIR". It was a can of corn, and of course...she drops it.

She picks up ball and tags runner coming from third.

Once fans get done screaming the normal "run, go back, throw it to first, step on the plate, do a summersault, play leap-frog, etc." I explain to coach that I said infield fly if fair, batter-runner is out, runner from third is out on tag.

He doesn't say anything, probably because of score...he won 13-0 in 5 innings (and 55 minutes, thank you very much).

He asked this question after the game:

If I don't call it, is it still an infield fly? I said yes it is, because players and coaches should know the situation.

Was I right?