One thing that seems to be lost in this discussion is the apparent belief that the Patriots should be able to sign every free agent they desire. News flash: 31 other team are selling those same free agents on why they should sign with their team, selling their city/region, coaching staff, team, etc. There are going to be multiple instances when a player finds another team to be a better fit or opportunity, or offer more job security.
This isn't baseball, where a handful of teams can outspend 90% of the rest of the league in order to build the best roster. The number of teams that have tried that approach and failed is lengthy.
I also have to question the concept that it is better to go 'all-in' for a single season with the idea that you realize it will screw you for several seasons. There is no guarantee that concept will work; we've seen that go up in flames in recent years with Philadelphia's Dream Team, the Dolphins, Bills and Jets being declared pre-season division winners (or more), the Vikings advancing to the Super Bowl by trading for Randy Moss, and going further back Oakland, Dallas and Washington trying that approach multiple times. There are only two teams that I can think of that went 'all-in' and won it all, and both happened over a decade ago: the Bucs in 2002, and the Ravens in 2000. It looks to me that the balanced approach - even when you have a star player approaching the end of his career - has a better success rate.
The biggest reasons why the Patriots have unspent cap money is because of Logan Mankins and Tommy Kelly. Thoughts on those negotiations have been debated in other threads - personally I do believe the Pats botched things with Kelly, and should have done something to keep him - though admittedly, none of us know exactly what Kelly said that caused the Patriots to agree to release him. In regards to Mankins, negotiations for a restructure had been ongoing for a while. Perhaps based on early talks the Pats were confident an agreement could be worked out. Obviously a trade that late in the year was not the preferred option.
In terms of signing other players, also keep in mind that close to $15 million of the 2014 cap is being used up on one player on IR and another that is in jail. That's a fairly sizable handicap to overcome. Having several highly productive players on rookie contracts is extremely beneficial to a team's success. But before someone blasts the Patriots for their draft picks, consider how cyclical that is. There was a time when the Ravens were the gold standard, but after selecting Sergio Kindle and some others that led to an 8-8 season that talk quieted down. The Packers were the flavor of the month for a while, but folks stopped holding them up after seeing early picks spent on guys like Brian Brohm, Patrick Lee, Mike Neal, etc., and a defense that allowed 27 points per game.
Winning a championship in the NFL is extremely difficult to do, thanks in part to so many variables such as injuries, fluky bounces, tipped balls and questionable penalties. Add in the double-edged sword of free agency and a true salary cap to what is by far biggest 'team' sport - where success is comparatively more dependent on the entire team rather than on one single player - and it boggles my mind how some expect/demand a franchise to field the best team in the league each and every year.