ARLINGTON -- By the end, it was a straight-up classic, a made-for-NFL Films afternoon, the kind of wildly entertaining three hours that keeps us all coming back for more. It was the equal of this franchise's first playoff, an NFL championship against Green Bay in the Cotton Bowl that just passed its 50th anniversary. And it contained more drama than the Ice Bowl a year later, even if the bad weather here arrived after the game, preventing some fans from leaving AT&T Stadium two hours after the Packers' 34-31 triumph.

A frustrating loss for Dallas, more disappointment than a sign of failure in most views (including this one), extended this club's streak of not having reached an NFC title game to 21 years. That's what separates this loss from those ancient defeats to Green Bay. The Super Bowl was just one step away back then. This team, setting records in the process of a 13-3 season, came no closer to the Super Bowl than the 2014 team that was thwarted by the same nemesis.

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So let's face it, some of this is just about the right arm of Aaron Rodgers, a man Cowboys coach Jason Garrett labeled as one of the three best quarterbacks ever to play the game. There was no evidence Rodgers was anything less than that Sunday as he riddled the Cowboys' defense with four long touchdown drives in the first 34 minutes, then produced the plays needed for two Mason Crosby field goals in the final quarter.

"I felt good. I felt very calm," said Rodgers, who threw for 356 yards. "I don't think anyone doubted we were going to score on those last two drives."

For Rodgers and the Packers, it's on to Atlanta for a game of who-can-top-this fireworks with Matt Ryan.

For the Cowboys it's over. And Garrett said he starts thinking about 2017 on Monday, which is every bit as depressing as it sounds.

For Cowboys fans, it's a not so simple question. When does the feeling of failure or at least of missed opportunity start to fade away? Unlike the 2014 team the Cowboys hoped to emulate in drafting Ezekiel Elliott, this team earned the No. 1 seed in the NFC. They saw key player after key player fall for enemy teams (Seattle safety Earl Thomas, Packers wide receiver Jordy Nelson) while the Cowboys arrived here Sunday healthier than they were in Week 1.

Even owner Jerry Jones, who might find himself voted into the Pro Football Hall of Fame in three weeks, isn't sure when the pain subsides.

"I really can't say we should have won the game. But after the second half, I saw that we were an even better club than I thought we were," Jones said. "So for that, I'm terribly disappointed right now. I don't know that any words can be said about missing this opportunity."

Garrett spoke of being proud to be part of this group even if it came up short of the goal, and you can't fault him for that. Now if the second half had looked like the first half when the Packers grabbed a 21-3 lead before the Cowboys got anything going, we would be talking about a team that collapsed under pressure.

This team was down 15 points entering the fourth quarter, and Dak Prescott drove the team 59 and 80 yards for touchdowns, then scored the much needed conversion by himself on a quarterback draw with just over four minutes to play.

Only in a game that features Rodgers would there be time for three field goals after the two-minute warning.

Rod Marinelli's defense, much more the pretender than the contender in the opening half, made plays late in the game that would have sent a more ordinary matchup to overtime. But you know all about Rodgers and his penchant for delivering "Hail Mary" plays. It was with that in mind with 12 seconds to go from his 32 that he found his tight end Jared Cook for 36 yards just inside the out-of-bounds line. Mason Crosby's 51-yard field goal just 1:38 after a 56-yard kick that preceded Dan Bailey's 52-yard boot ended the kickers' showcase and the Cowboys' season.

Officially, it ends with back-to-back losses. But one in Philadelphia meant nothing and this one at home against a Green Bay team without Rodgers' favorite target means everything.

"That's the best team I've ever been around, and for it to end like that it's heartbreaking," said safety Barry Church, whose huge third-down sack of Rodgers stalled the Packers' possession just before Prescott tied the score.

A young team with a bright future will be picked by many to win the NFC in 2017. To everyone but Garrett, that's not going to feel like anything but the distant future as Cowboys' fans attempt to distinguish an incredible season from a shocking finish.

Twitter: @TimCowlishaw