"You've got to be careful to turn around the day after and make decisions that aren't well-thought out," Payton said. "There were more wide lefts than just the kicker."
Carney played in 11 games for the Saints last season and connected on 13 of 17 field-goal attempts. He then became a consultant with the team.
Atlanta rushed for 202 yards, converted 9 of 18 third downs and limited New Orleans 43 rushing yards, continuing three early season themes for the Saints.
The Saints are last in the NFL in rushing, averaging 57.3 yards per game. They are third-to-last in rushing defense, allowing 145 yards per game. Opponents have converted 47.5 percent of their third downs, the fourth-highest total in the league.
"It's an execution problem," linebacker Jonathan Vilma said. "I wouldn't say it's been mental breakdowns because that means you're not on the right guy or something else. We are calling the right plays. We're just not executing."
Atlanta scored a touchdown in the first half on a 19-play drive that featured two third-down and two fourth-down conversions.
Falcons tight end Tony Gonzalez converted five third downs and one fourth down with his catches, another early season issue for the Saints. Gonzalez finished with a team-high 110 yards on eight receptions, following Minnesota's Visanthe Shiancoe (four catches, 76 yards) and San Francisco's Vernon Davis (four catches, 78 yards), who also had team highs for yards against New Orleans.
While the Falcons churned out 25 first downs, the Saints went virtually nowhere on the ground. Pierre Thomas had nine carries for 30 yards before exiting with an ankle injury in the fourth quarter. Rookie Chris Ivory, who missed the first two games with a knee injury, debuted with 13 yards on seven attempts and lost a fumble.
"We are going to need to be able to run the ball more efficiently to have the success we hope to have," Payton said. "We are going to need to defend the run more efficiently, too. Those are two important components to winning."
Despite those concerns, the Saints would be undefeated had Hartley not blown the short field-goal try in OT. Entering the softest part of its schedule -- Carolina, Arizona, Tampa Bay and Cleveland are up next -- New Orleans could have been in position to repeat its 2009 run as the wire-to-wire leader in the NFC South.
"That's the most frustrating part," Shanle said. "We could have gotten some nice separation early in the season. There's not going to be any panic, but it's hard because this one got away from us."
For the second consecutive day Monday, Hartley answered every question about what went wrong and how secure he felt about his future as the Saint' kicker.
"At this position, sometimes you're the hero and sometimes you're the goat," he said. "Last night, I was wearing the horns. I'm still the starting kicker for this team, and I'm going to prepare like that."
Notes: Payton said the Saints wouldn't have an injury update until Wednesday. In addition to Thomas, Porter tweaked a hamstring in the first half but returned in overtime. Safety Roman Harper suffered a thigh bruise in the first half and didn't return. ... Payton said he hadn't lost confidence in Ivory, adding the rookie would have seven to 10 carries per game while Bush is out.
The Associated Press contributed to this report.