Last year, once eliminated from the playoffs and losing I believe 6 in a row, the Giants went onto to beat 3 teams by double digits and nearly beat the division leading Eagles if not for some special teams misques
2013, once eliminated from the playoffs, they went onto win the last 2 games of the year, with one of them being against Detroit, who was still in the playoff hunt at the time
2012, they were not eliminated within the final game, but they were almost done with them needing a bunch of shit to happen. After losing a critical game against the Ravens, which could have put them into the playoffs, they went onto beat the Eagles 42-7 in the final game of the year.
These are the last 3 years, and they have missed the playoffs for 3 years in a row. They have played well, or at least better then they had previously in the past once they have been eliminated or nearly eliminated from the playoffs