GREEN BAY, Wis. — Micah Parsons called his teammates' performance, or lack thereof, “disgusting.”

Dallas Cowboys team owner Jerry Jones referenced the “frustration” six times in a span of 4 minutes and 2 seconds.

Quarterback Dak Prescott sat on the stool of his visitor’s locker with his head down and his stare vacant.

And head coach Mike McCarthy — in his third year at the Cowboys' helm, returning to the home where he spent 13 years in charge — declined to further elaborate on nostalgia.

“I’m not trying to be rude,” McCarthy said after a 31-28 overtime loss to the Green Bay Packers. “I am humble-pied out.”

The Cowboys fell short in two meaningful realms Sunday. They failed to secure a victory for McCarthy to help overwrite memories of a brutal 2018 midseason dismissal, and they failed to show the NFL that maybe, just maybe, for the first time in more than two decades they’re enough of a complete and disciplined squad to threaten in the postseason.

At 6-3 and third place in the NFC East, the Cowboys still hold a 95% chance to make the playoffs, per FiveThirtyEight's playoff predictor model. But Sunday’s loss raised major questions about whether they would likely advance.

“It’s bad,” said Parsons, the favorite for NFL Defensive Player of the Year. “You’ve got to be able to finish games in this league, especially against guys like [Aaron] Rodgers. You got to be able to finish.

“Finish, finish, finish — that’s what this game’s about.”

Unfinished business

The Cowboys were confident when they tied the game just before halftime and confident when they leapt to a 14-point lead in the third quarter. Even as the Packers whittled away at that edge — and ultimately tied the game with 2:33 to play in regulation — the Cowboys believed their balanced offensive attack and dominant pass rush could endure the Packers’ surge.

In overtime, Tony Pollard bit off a pair of 7-yard runs. Prescott and CeeDee Lamb connected on a crosser route similar to the play they’d botched on Prescott’s second interception in the second quarter. And then the Cowboys’ system went awry.

Pollard’s chain-moving 6-yard run was called back when rookie receiver Jalen Tolbert lined up offsides, violating the neutral zone. Cowboys RB3 Malik Davis’ impressive 16-yard gash was negated by left guard Connor McGovern’s holding flag. Prescott found tight end Dalton Schultz to narrow a second-and-19 to third-and-3. But then the attack that had surpassed 200 yards on the ground attempted to throw, Lamb grazing the ball with both hands but ultimately not securing the crosser. McCarthy signaled the Cowboys to go for it on fourth-and-3, but Prescott’s last-ditch attempt under heavy pressure fell short.

A red-faced McCarthy slammed his headset to the ground.

“I am very frustrated with the end of the game, obviously,” McCarthy said. “We need these tight games to get to where you want to go. I thought we were in total control, but in overtime you know obviously the penalties and things.”

McCarthy’s volume and intensity escalated uncharacteristically with each of his next three words.

“Very, very, very frustrating,” he said. “But you have to overcome those things.”

McCarthy reiterated his belief that they “needed to go for it” on fourth down, a decision he made on second down after seeing the rickety, penalty-ridden drive unfold.

“So our feeling was just keep playing,” he said. “We had good calls. I’m fine with the decision.”

Two runs and a 36-yard completion on an RPO afterward, the Packers comfortably reached field-goal range.

Rodgers downplayed the victory against his former coach, fake-checking the box score as he asserted, “I don’t think Mike suited up.” Even so, in establishing a dangerous connection with a young receiver and snapping the five-game skid, Rodgers said there were “a lot of demons that were exorcized today.” He didn’t just silence internal doubts after rebounding from a one-touchdown, three-interception loss against the Detroit Lions to a three-touchdown, no-interception win against the Cowboys.

“The little voice in your head that tries to knock you off that confident perch that you’re on?” Rodgers said. “I knocked that voice back into hell and had a good performance today.”

A weekly weakness

Rodgers made well-timed, efficient throws, including rookie second-round receiver Christian Watson’s first career touchdown — and his second and third. He burned the Cowboys with 58- and 39-yard scoring strikes. In overtime, too, Rodgers’ execution of the RPO to find receiver Allen Lazard for a chunk gain was masterful.

But the Cowboys defense’s top issue wasn’t Rodgers’ 14 completions or 224 yards. They failed to withstand the Packers’ rally, in large part, because they allowed the tandem of Aaron Jones and AJ Dillon to gash them for more than 200 rushing yards and nearly 5.5 yards per carry.

In the fourth quarter, that punishment reached an 8.2-yards-a-pop tenor. The Cowboys failed to force third-and-long situations, the Packers neutralizing the pass rush that has carried the unit. Dallas’ run defense was already a weak link entering the game, and the team knows it's exposed ahead of a three-week stretch in which the Minnesota Vikings’ Dalvin Cook, New York Giants’ Saquon Barkley and Indianapolis Colts’ Jonathan Taylor loom.

“Nobody’s going to allow us just to rush, nobody’s going to allow us to just be who we are,” Parsons said. “That’s why we’ve got to take out this fire. Until we take out this fire, we’re going to just keep seeing it.”

The Chicago Bears, too, rushed for 200 yards in the Cowboys’ last outing.

“If people want to keep doing their own thing, we’re going to deal with this all year and we’re going to never be the team that we’re going to want to be,” Parsons said. “We have to put this out. We have to be accountable. We have to stay on our gaps and stop the run. Then once we stop it, we can go back to being who we are.

“But until we do that, it’s going to be a long year.”

Or, in some ways, perhaps a shorter one.

Because the Cowboys know their inability to stuff the run will preclude any deep postseason success. And a regular-season run has lost meaning.

Dallas has rarely been awful in recent years but has regularly been mediocre during the 26 seasons since the franchise last reached a Super Bowl or even an NFC Championship game. Dominant regular-season wins against lesser teams — think, their 49-29 dismantling of the Bears two weeks prior — have instilled facades of confidence that are tested against top quarterbacks and in hostile road environments like last month’s visit to Philadelphia and this weekend’s to Green Bay.

The Packers have now beaten the Cowboys in nine of their past 10 outings, including playoffs. Dallas doesn’t have enough cushion to withstand the offense’s mistimed and miscommunicated interceptions, the leaky yardage and poorly fitted run pursuits the defense has.

In what seems like a Cowboys tradition against Rodgers, Dallas played hard but left itself too little room for error. It’s something “this team will have to overcome,” Jerry Jones said.

“We wanted to get it for Mike, but more importantly, we wanted to lay another brick to where we’re going and we didn’t do that,” Prescott said. “We didn’t take that step we’ve talked about.”

Follow Yahoo Sports’ Jori Epstein on Twitter @JoriEpstein