On paper, the Saints trailed the two teams ahead of them in the NFC South standings as of Monday by one win.

However, unless they vastly improve the way they’ve played in losing three of their first four games this season, the Saints know the distance between them and Atlanta and Carolina (both 2-2) will only grow as their season progresses.

“This team — bottom line — has not found what it has to do to win, and that’s what we need to search for right now,” veteran tackle and Saints offensive captain Zach Strief said Monday. “It’s very simple: You have to work harder. Everybody does.”

Strief, his coach and several of his teammates met with reporters at the Saints training facility a day after they were dealt a 38-17 loss by the Dallas Cowboys at AT&T Stadium in Arlington, Texas.

The Saints defense allowed Cowboys running back DeMarco Murray to rush for 149 yards and two touchdowns off 24 carries. Dallas quarterback Tony Romo was 22-of-29 passing for 262 yards and three touchdowns.

The New Orleans defense had no takeaways.

Meanwhile, the Saints offense turned the ball over three times and missed a 41-yard field goal. The team faced a 24-0 halftime deficit before offering the ineffective resistance it did with a field goal by Shayne Graham and one touchdown catch each by tight ends Josh Hill and Jimmy Graham in the third and fourth quarters.

That performance against Dallas followed defeats of 37-34 in Atlanta (2-2) and 26-24 in Cleveland (1-2) in Weeks 1 and 2. Though a 20-9 victory at home against 2-2 Minnesota was sandwiched in between those losses and Sunday’s, that did little to mask the myriad issues plaguing the Saints.

Chief among those issues was a turnover ratio of minus-six (one takeaway on defense all the way back in the first quarter of Week 1, and seven giveaways on offense), worse than 30 NFL teams Monday afternoon. Another was a defense that was surrendering the fourth-most yards (396) and tied for the fifth-most points (27.5) per game in the NFL.

All of that was enough to convince the Saints they had to strictly focus on bettering themselves before they could worry about closing the mathematically slim cushion Atlanta and Carolina had at the top of their division or aspire to distance themselves from Tampa Bay (1-3), which they meet in the Mercedes-Benz Superdome this Sunday.

Teams that clinch their division are guaranteed to host at least one playoff game, which is a perennial priority for a franchise like the Saints, who didn’t win their first true road postseason contest until they beat Philadelphia in the wild-card round Jan. 4.

“If we continue to play the way we’re playing, then results will be back and forth, and we’ll be sitting here with a 7-9 (or) an 8-8 record” to most likely miss the postseason, Saints coach Sean Payton said. “There has to be a sense of urgency to clean up these mistakes we’re discussing, improve in some of these areas, and all that other stuff will take care of itself. It’s all out there.”

Saints linebacker and defensive captain Junior Galette added “nothing’s encouraging” about the way New Orleans has defended in its three losses, not even in a division race that for the moment at least is jumbled.

One deficiency that strikes close to the heart of the proud pass-rusher Galette is the fact that the Saints have registered only five quarterback sacks and 16 quarterback hits, numbers that illustrate the struggles New Orleans has had at creating pressure on the opponents’ signal-callers, something that in turn often produces takeaways.

Galette has accounted for two of his team’s sacks and six of the quarterback hits to lead the Saints.

“You have to be realistic and know that we’re not as good as we thought we were,” Galette said about a team many assumed would be able to repeat the performance that in 2013 enabled it to field the fourth-stingiest defense in the NFL.

He added that the season is not over and that the team had not abandoned its belief that “the sky is the limit.”

But for now, Galette said, “We’re not looking at other teams. We’re looking at ourselves.”

Punter and special-teams captain Thomas Morstead agreed with his fellow Saints’ refusal to go easier on themselves because no one had managed to seize a commanding lead in the NFC South.

“It doesn’t make you feel any better about the (losses),” said Morstead, who drew praise from Payton for giving the Saints’ defense favorable field position Sunday with one punt each to the Cowboys’ 11 and 23.

However, Morstead said, “It’s nice knowing there’s not a 4-0 team in front of us.”