IRVING, Texas — The Dallas Cowboys now must try to keep their season from slipping out of reach.

They were so close — by the length of Dez Bryant's fingertips — to being within a half-game of the NFC East lead and having a vital tiebreaker with a season sweep of the division-leading New York Giants. But the receiver's touchdown catch in the closing seconds was overturned on a replay review.

Dallas (3-4) hits the halfway mark of its schedule Sunday night at Atlanta (7-0), the NFL's only undefeated team. The Cowboys then go to Philadelphia for the first of two meetings in four weeks against their division foe.

"There is a tremendous amount of urgency," coach Jason Garrett said Monday. "Every game is critical. This is a big game."

The Cowboys overcame an early 23-0 deficit and led going into the fourth quarter Sunday in what would have been the biggest comeback victory in team history.

But New York won 29-24 after regaining the lead with two field goals, the go-ahead points coming after Felix Jones fumbled. The Giants held on after replay showed Bryant's fingers hit out of bounds before he landed on a leaping 37-yard grab with 10 seconds left.

Tight end Jason Witten's franchise-record 18 catches and Tony Romo's career-high 437 yards passing on a record 62 attempts (with 36 completions) weren't enough to help the Cowboys overcome six turnovers, including four interceptions.

New York (6-2) now has a firm grasp on the NFC East lead because no other team in the division has a winning record. Philadelphia (3-4) and Washington (3-5) both lost Sunday.

"It's to that point in the season where you don't have time," Witten said. "Nobody cares about battling. They don't, they want to see you win. ... The clock's ticking. You have to be able to find a way to get on top here a little bit."

Romo has already thrown an NFL-high 13 interceptions in 283 attempts, after having only 10 picks in 522 throws last season. The Cowboys have 19 total giveaways and a minus-11 turnover margin.

Asked how much turnovers have contributed to the Cowboys' losses, Garrett responded, "I think it's probably been the biggest single factor."

Dallas keeps turning it over despite a continued emphasis to correct that problem, a fact that led to a rare public admission by Garrett of being frustrated.

"In this particular case, absolutely," Garrett said. "Frustration is not a helpful emotion, but it's something that we just have to continue to focus on and get better at. ... At times, we've done a very good job of it, and I think the results speak for themselves. Other times we haven't, and similarly the results speak for themselves."

While Bryant almost had a decisive play, and finished with five catches for 110 yards, he contributed to two early turnovers that helped the Giants lead 23-0 only 2 minutes into the second quarter.

Romo was trying to throw deep when Bryant rounded his route instead of flattening out across the middle. Stevie Brown cut in front of him for an interception.

Bryant later fielded a punt over his head. Even though he recovered after the ball went through his hands, Bryant was stripped and fumbled inside the Cowboys 20.

"Certainly, the play he had (Sunday) was not a good play for our football team," Garrett said. "We've got to take care of the football on offense, we've got to get the ball on defense, and we certainly have to do that on special teams as well."

Cowboys leading rusher DeMarco Murray could be back against Atlanta after missing the last two games with a sprained right foot. When Murray walked in the locker room briefly Monday while it was open to the media, he wouldn't directly answer if he thought he would play Sunday night.

"We'll just have to wait and see. It seems like he's moving around a little bit better," Garrett said. "That's an injury you have to be patient with. We don't want to rush him back, then take any backward steps."

It could be a big boost if Murray can play, considering Jones had 13 carries for 19 yards against the Giants. Phillip Tanner gained nothing on two carries on consecutive plays after Dallas had first-and-goal from the New York 1 early in the third quarter.

When the Cowboys were driving in the final minutes with all three timeouts left, they didn't even try to run after second-and-1 from the 19. Instead, Romo threw consecutive incompletions before an interception.

"They were pretty committed to stopping the run," Garrett said when asked about the play-calling. "Certainly whenever the play doesn't work, it's easy for us as coaches to look back afterward and say we should have done something different."