The Pats should not be overlooking anyone. They are 7-7 in the playoffs since they won SB 39. They done plenty of choking themselves.
I think people have been so spoiled for so long that they forget just how difficult it is to win in the play-offs.
Obviously when you're stringing together championships, you're going to have a great play-off record. But being around .500 in the playoffs without winning a championship isn't actually terrible. In fact, a lot of Super Bowl winning teams are around that mark after the fact.
A SB win inflates the record, but every other play-off team that doesn't win looks statistically similar. A top seed that goes to the Super Bowl and loses will finish 2-1, while a team that gets killed in the wildcard round will be 0-1; not a huge variance here due to the small sample sizes.
The Packers are 1-2 in the play-offs since winning it all. The Saints are 1-2. The Bucs are 0-2, having only played in 2 play-off games since their 2002 win. The Steelers are 2-2 since their last SB. If you include their last SB run as an extension of their first SB run, you could say they're 6-3, but they also missed the play-offs 3 of those years too, and again, outside of the Super Bowl runs, they're 2-3. Super Bowl runs = significant boost to record. All others rarely see it.
After Peyton Manning finally won a SB, he went 2-4 with the Colts (those 2 wins being part of their second Super Bowl run, where they finished 2-1). The Colts and Manning are both now 2-5 since the SB win with this season's losses to Baltimore.
The Ravens went 6-7 in the play-offs after winning the SB in 2000, but that didn't prevent them from running off 4 wins in a row, although they were also a minute away from being 1-1.
If we look solely at records, the Giants are probably the best example, but part of that is because they didn't get to play many play-off games after winning a SB. They went 0-1 in the 2008 playoffs after winning in 2007, then missed the play-offs entirely in 2009 and 2010. After winning it all in 2011, they missed the play-offs again in 2012.
So really, pretty much every team that has won a Super Bowl has a record around .500 in the playoffs since that time, except for perhaps the Giants, who didn't even make the play-offs half the time. Only the SB winner gets to inflate their playoff mark by any significant margin. Some of those records even include SB runs, like Manning's second which still finished with only 1 game above the .500 mark.
I'm not saying we've been fantastic in the play-offs, just that to keep repeating the record over and over and over as proof of a massive choke job is disingenuous. The record really indicates that we haven't won a Super Bowl in a while. Let's not make it into something that it isn't.