Schiano did a whole lot with very little resources in Rutgers: not a big name school, not constantly on television, not a big name conference, no big name NFL stars for alumni, etc. Basically he overachieved and was far more successful than one could have reasonably expected in that position. It was somewhat like Steve Spurrier making Duke a winning football team, or when Northwestern won the Big Ten for the first time in sixty years. Okay, maybe not quite as dramatic as those two examples, but it was still a huge accomplishment.
The big question now will be whether or not he will be expected to do well with less resources than his competition. From the day Morris was hired Tampa Bay had one of the lowest, if not the lowest budget in the NFL. They're in a division that has to face Drew Brees, Matt Ryan and Cam Newton twice each, and they have the league's lowest payroll. If the organization continues to place profits over winning by spending as little money as they possibly can then Schiano is doomed to failure, no matter how good he is. If that's the way it plays out then maybe at that point Belichick will hire him to be part of his staff in Foxboro.
