The fact that Atlanta ended up needing to convert a more difficult 4th down conversion - and it wasn't surprising in the least - validates a lot of what Bill is suggesting.
THIS. If they thought this way in advance as Coach Belichick certainly would have, they would have tried for a quick 1st down on 3rd and 1and given themselves 2 chances to get 1 yard and thereby have more chances to get it in the end zone on that drive, given that they were so close with little time left. When 4th and 1 came around, they still should have gone for it. When Bill Belichick says that if you can't one yard when you need it, you don't deserve to win, he's not just talking in hyperbole, he's saying that you only get so many chances to make game-winning plays, and you should take those chances and win, if you intend on winning.
Teams take the easy points too often to keep hope alive, instead of being aggressive and trying to win. This goes for the first quarter as well as the 4th, if facing a high-powered offense. Being more aggressive is the starting point, but I think that would have been more valuable on 3rd down than 4th in this case. Knowing that you intend to go for it on 4th down makes it that much easier, because it gives you more options on 3rd down.
If you want to think clearly about strategy, you owe it to yourself to look at
Advanced NFL Stats 4th Down Calculator. This uses game logs from all games from ~1996 (when enforcement of passing rules started to change) to the present and calculates probabilities for points and liklihood of wins for any 4th down decision and the break-even success probability by which you can gauge whether it's worth going for it. (Granted, some of these are limited datasets and therefore some vagaries exist related to extreme results [e.g., turnovers, blocked field goals] that have occurred in specific situations, so play with it a bit and check-out some of the research on the subject.)
This is only a piece of the puzzle, as it doesn't account for how match-ups are going, but I think it makes a convincing argument that Smith should have gone for it on 4th and 1. All other things being equal, going for it on 4th down tripled the probability of the Falcons winning the game. That's not even close, and a coach should know that offhand when making his 3rd down call.