Head coach Tom Coughlin of the New York Giants walks...

Head coach Tom Coughlin of the New York Giants walks off the field after a loss against the San Francisco 49ers at MetLife Stadium on Sunday, Nov. 16, 2014 in East Rutherford, N.J. Credit: Jim McIsaac

As Odell Beckham Jr. came down with a fourth-quarter reception to set the Giants up with first-and-goal at the 4, Tom Coughlin said he thought it was going to be a season-changer.

"When he made that spectacular catch, I figured: This is going to be great!" Coughlin said. "We're going to win one of those nail-biters."

Almost exactly 24 hours later, he was still trying to explain how the Giants did not score in that situation, how they lost to the 49ers, and how monumentally un-great things are. And, like most of the Giants on Monday, he was coming to grips with a new reality.

Though there is still a mathematical possibility for them to reach the playoffs, it's an all but impossible goal from their current 3-7 position. A loss to the Cowboys on Sunday night coupled with a win by the Eagles over the Titans earlier in the day would eliminate the Giants from contention in the NFC East and, depending on outcomes around the conference, could even formally knock them out of the wild-card hunt.

The Giants could be turkeys for the second straight year, unable to survive past Thanksgiving.

Some of them seemed to be aware of their dismal circumstances.

"We're not handling it well," safety Quintin Demps said. "This one stings. They all sting, but this one stings a lot."

Others, though, cling to the threads of hope that still exist but are fraying quickly.

"We won't accept that," fullback Henry Hynoski said of the team's virtual elimination. "We're still fighting for the playoffs. That's our goal. The opportunity is still there. It won't settle in until after the season."

Running back Rashad Jennings, who overheard a reporter's question for Eli Manning about the team's undoubtedly dwindling playoff aspirations, interjected his own thoughts: "Reality is subjective."

What's not is that the Giants have lost five straight. And at this point, Coughlin and Manning both said the immediate goal of ending that skid supersedes any big-picture objectives.

"I think our concern is to try to get a win," Manning said. "After the run we had, just get a win, and get some positive energy, and feel excited about what we are doing . . . We've just got to put it all together and try to get a win this weekend against the Cowboys."

Coughlin pointed out that the defense was able to rebound from its performance against the Seahawks and come back focused and energized against the 49ers. He told the team he hopes that the offense can do the same this week.

If they do, and the Giants can beat the Cowboys, it likely still won't be enough to salvage the season. A season that came down to those four plays from the 4-yard line.

After watching the video, Coughlin said he thought two of them -- the fade passes to Rueben Randle and Larry Donnell on second and third downs -- "should have been caught." He also strongly hinted that a penalty should have been thrown on the one to Donnell.

Ultimately, Coughlin said that series of plays will stick with him.

"Why wouldn't it?" he said. "The ball is on the 4-yard line. You have a chance to win the game. Somebody make a play. Get the ball in the end zone and we win.

"I'll remember that one."

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