As a Packers fan, I've witnessed several missed calls both for and against that helped send us to a super bowl and prevented it. Seattle and Dallas games come to mind.
Rather than giving an apology for a blown call, since this event happens every single year, I would like to see the NFL actually take some action. Maybe place an official in the press booth. Maybe make all plays reviewable. Certainly their sponsorship would love the additional time created for more commercials.
Apologizing for blatant errors is like sending prayers to hurricane victims! What they need is a fix action!