Again, that ignores whether or not he shouted out "Infield fly!" before the sign was made. Sixty thousand screaming fans wouldn't have heard it, but the 12 or so players on the phone field would have.
I've umpired. Umpires are trained to shout out as they make the signal. No umpire would shout out and make the signal seconds later and certainly NO major league umpire would do so. Unless it's windy the call is usually made before the fly ball reaches it's apex. This play was a hot topic among umpires and the three other umps I discussed this with plus several baseball coaches all agreed the call was muffed. Your love for the Cardinals is making you biased.
And no, the players would not have heard the ump over the crowd noise.