The Giants were eliminated from the NFC East on Sunday despite blowing out the Washington Redskins.
The Cowboys' 29-23 overtime win over the Eagles put the Giants three games back with three games to go, and the Giants would not be able to hold the tiebreaker over Dallas even if they won their Week 17 matchup.
At 5-8, the Giants would need a miracle to clinch a wild-card berth. The Seahawks (7-5) and Vikings (6-5-1) currently hold the last two playoff spots in the NFC.
New York would also need to climb over the Panthers (6-7), Eagles (6-7), Redskins (6-7), Packers (5-7-1) and Buccaneers (5-8), who currently hold the tiebreak over the Giants based on winning percentage in conference games.
The Giants are currently in line for the No. 9 pick in the NFL draft.