EAST RUTHERFORD, N.J. — The New York Giants have faced and overcome adversity before under head coach Tom Coughlin, but the team faces a particularly daunting challenge this week.

New York is preparing to face a red-hot Dallas Cowboys team that is coming off a big 30-23 win against the defending Super Bowl champion Seattle Seahawks on the road.

That win put the Cowboys atop of the NFC East at 5-1 with a chance to create distance from the Philadelphia Eagles, also 5-1, who have a bye this weekend.

The Giants, who currently sit 3-3 and in third place in the NFC East, have not defeated a team with a winning record.

A loss to the Cowboys on Sunday would not only put them into a deeper hole before the bye week in that they would be 1-2 against their division opponents, it could potentially be the final nail in their 2014 season.

After the Giants return from their bye week, they will face a grueling four-week schedule that includes meetings with the Colts, Seahawks, 49ers and Cowboys – all teams with winning records.

To make matters worse for the Giants, who are desperately trying to put their embarrassing 27-0 loss to the Eagles last week behind them, they will need to carry on without receiver Victor Cruz, who is out for the season after having open surgery to repair a torn patellar tendon in his right knee.

The Giants, who spent much of last week puffing out their chests and running their mouths, will not be making that same mistake again this week. Quarterback Eli Manning and defensive end Mathias Kiwanuka, two of the longest-tenured members of the team, both urged their teammates to “grow up,” a sentiment that Coughlin fully backs.

“As a team, I personally felt like we weren’t as focused as we could have been last weekend,” the head coach said. “I did not think we reacted well to adversity during the game. Some of that concept that we talk about – team – has got to develop and grow.”

Coughlin’s message to the Giants this week has been to leave the past in the past but to learn from the mistakes and focus on the next challenge.

That won’t be easy. The Cowboys have a stellar offensive line unit that has helped contributed to running back DeMarco Murray rushing for 100-plus yards in each game this season. Murray currently leads the NFL in rushing yards with 785.

In the passing game, quarterback Tony Romo has also been on a hot streak. He is completing 68.6 percent of his pass attempts, is averaging 7.9 yards per pass attempt, and is third on the Cowboys in rushing with 11 carries for 33 yards.

“He buys more time down the field and usually the ball goes deep down the field,” Coughlin said of Romo’s scrambling ability. “He’s demonstrated that ability over and over.”

While no challenge is insurmountable, Coughlin did hint to having some concern about how his team might respond given the recent events – especially the sight and sounds of hearing Cruz scream in pain and then sob uncontrollably as he was carted off the field.

“There’s a lot of things we’re trying to deal with right now, to be honest with you,” Coughlin said, admitting that the devastating loss of Cruz is one.

So what then do the Giants do to make sure they do not let what happened last week linger?

“You deal with it on Monday, you watch the film, you try to make some corrections, and by Tuesday you’re preparing for the next opponent,” said quarterback Eli Manning.

“It doesn’t take long when you’ve got another division rival coming up, another big game for us. We’re getting ready for Dallas and we’re moving on.”

“I expect us to go in and play with some pride, play with some dignity, said safety Antrel Rolle.

“Focus,” added defensive end Jason Pierre-Paul. “Just come in, and what you do in practice is what you are going to do in the game. We come in and practice and make sure we execute our plays and talk.”

Manning believes the Giants will be able to find that resiliency that was lost last week and take care of business.

“Yeah, I expect us to do that. I think we’ve responded well to the losses when we’ve had them or when we’ve had a tough game this year. We know we have to play better than we did.

“We’ve got to figure out how to move the ball and be more successful and stop having the mistakes that hurt us last week. I think we’ll do that. We have a tough challenge ahead of us, they’re playing great football and we’ve got to play to their level.”

SERIES HISTORY: 104th regular-season meeting. Cowboys lead series, 59-42-2. The Giants have won four out of the last five played at Dallas, and are 19-32-1 all-time in regular-season road games vs. the Cowboys.

–WR Victor Cruz was released from the Hospital for Special Surgery in Manhattan. He stopped by the team’s headquarters for a brief visit before being whisked away in a limo. Coughlin said he spoke at length with Cruz on Tuesday and that the receiver was in good spirits.

MEDICAL WATCH: LB Jon Beason came through Sunday’s game with some soreness, but no setbacks. He took his full workload in practice for the first time this season. … LB Spencer Paysinger (hamstring) was limited in Wednesday’s practice. Paysinger missed last week’s game after not being able to practice. … CB Dominique Rodgers-Cromartie (back/hamstring) did not practice on Wednesday and has failed to finish the past two games.

GAME PLAN: The Giants need to go back to the basics of what got them on their three-game winning streak, especially given the injury situation on both sides of the ball.

On offense, New York got away from throwing the short, quick passes last week with the hopes of exploiting the Eagles secondary. That didn’t materialize, largely because the Giants offensive struggled to sustain blocks on the deeper quarterback drop-backs. The plan backfired as New York gave up eight sacks.

On defense, the Giants’ blitz has to get home with the front four, something that it was unable to do with much success last week. By sending an extra blitzer, the Giants left themselves vulnerable in the middle of the field.

That can’t happen this week. Although tight end Jason Witten isn’t putting up the numbers he once did, he has traditionally hurt New York by working the middle of the field.

MATCHUPS TO WATCH:

Giants MLB Jon Beason vs. Cowboys RB DeMarco Murray, who leads the league with 785 yards rushing: The Giants’ defensive co-captain and middle linebacker returned after three games following the aggravating of his toe injury in Week 2, but the effects of his absence showed up, especially in run defense where he was not as crisp as he usually is. This week he will go against Murray, who has six straight 100-yard rushing performances this season while averaging 5.0 yards per carry.

Giants DE Mathias Kiwanuka vs. Cowboys OT Jeremy Parnell. The Cowboys will be without starting right tackle Doug Free for approximately three to four weeks because of a fractured foot. Free will be replaced by Parnell, who has taken 43 snaps over the last two seasons and who has just two career starts. He will go up against Kiwanuka, who has 16 tackles, 1.5 sacks and one tackle for a loss this season. Kiwanuka has struggled over the past two seasons against solo blocking, but if he can he take advantage of this matchup to get pressure on Tony Romo and the Cowboys backfield, it could be a big boost to a defensive line looking to rebound from last week.