"At this point, we can only focus on Washington. There is no 'what if.' We're going out there to win," Beckham said. "If our season is over, I'm making sure somebody else is coming home with us. That is the goal.
"The goal is to win all these games and see what happens, but if not, you have a tough game to play against us for the last four games."
The Giants are technically still alive in the race for the NFC East crown or a wild-card spot, but they need a minor miracle to make the postseason. ESPN's Football Power Index has them at less than 1 percent to make the postseason despite having won three of their past four games.
They can blame that on a slow start to the season in which they lost seven of their first eight games. The Giants have also lost all four of their division games this season.
The Cowboys (7-5) lead the division, one game ahead of Washington and Philadelphia.
With two division games remaining, the Giants are going to play a part in deciding who takes home the title. Beckham seems to see some peripheral benefit in beating the Giants' divisional rivals down the stretch, even if coach Pat Shurmur views it differently.
"I don't know what the spoiler thing means," Shurmur said earlier in the week. "I'm looking at the positive approach of us winning. I'm not really worried about the team we're playing, whether we hurt their chances to do something else. What I want to do is to be better than the team we're playing this Sunday."
The Giants are looking at their late-season surge as a potential building block. Shurmur believes the experience of winning late this year can carry over to next season.
Beckham, who has 77 receptions for 1,052 yards this season, likes what he has seen since the bye week last month.
"Since the bye week, we're playing at a very, very high level," he said. "I just hope we can continue that. That is all we can do at this point. Leave the rest of the season up to everybody else and focus on what we can control, which is winning our game and seeing what happens. Not really much more to say than that."