I'll try to convince you of the opposite. There's no "different," "special feel," "energy." Every team that has a good regular season and every fan of that team feels that way. There were loads of posts using those words here in 2007, 2009, and 2014. Winning does that to people: they think the excitement and energy and happy clubhouse are the causes of winning rather than the effects.
The only proven way to have success in the playoffs is to reach the playoffs consistently. You're very unlikely to win the SB in any given year: the other teams are good too. And it's rare that you'll build a powerhouse at the exact moment that the other teams are down, although the Patriots seem to luck into one easy playoff game every year. All you can do is build a team that contends every year and hope that the breaks go your way in the postseason. One year, they probably will. Other years, Mason Crosby hits the sorriest-looking 56-yard FG ever to make it through the uprights.
The good news is that this is a team built to contend every year for quite a while now.