"Unfortunately, the turnovers far outshadow the rest," Brees said.
Brees threw a career-high five interceptions and his record touchdown streak ended in New Orleans' 23-13 loss to Atlanta on Thursday night.
The Saints (5-7) have dropped two in a row, pushing them to the edge of the playoff race, and they know winning their final four regular-season games still might not be enough to make the postseason.
"The future as far as the playoffs goes looks pretty bleak right now," assistant head coach Joe Vitt said.
The Saints fell behind 17-0 before scoring 13 unanswered points to get back in the game. William Moore's two interceptions stopped the New Orleans comeback.
Brees' five-interception game came four days after he had two passes picked off and returned for touchdowns in a loss to San Francisco.
"A couple of critical mistakes cost us the game, and I'm OK saying that because I hold myself accountable," Brees said. "Really there have been some critical mistakes in the last two weeks that have cost us dearly."
He had never before thrown more than four interceptions in a game.
"That's the first time that's ever happened to me, so that's extremely disappointing," Brees said. "I pride myself on being a good decision-maker and not someone who will be a detriment to the game."
Brees had thrown a touchdown pass in 54 consecutive games. He broke Johnny Unitas' long-standing record earlier this season.
"I realize that. I guess records are made to be broken and at some point they come to an end," he said. "I felt like we could have taken that one for a while."
Brees' scoring pass to Darren Sproles late in the first half was nullified by a penalty. Lance Moore dropped a ball in the end zone.
Falcons coach Mike Smith said Brees' streak was "unbelievable."
"Drew Brees is an outstanding quarterback," Smith said. "The way the defense played tonight speaks volumes. The guys had gone out there and thrown touchdown after touchdown game after game after game."
New Orleans had won four in a row in the series.
Mark Ingram scored on a 1-yard run in the second quarter for the Saints' only touchdown. Garrett Hartley kicked two field goals.
The Falcons (11-1) will clinch the NFC South with a month to go if Tampa Bay loses at Denver on Sunday.
After Sproles' TD was wiped off the board, Brees allowed the clock to run out in the first half when the Saints had the ball inside the Atlanta 10. Time ran out following a short pass to Sproles.
"Obviously we were going down to get some points in the 2-minute drill," Brees said. "Honestly I thought we had more time than we did. The last time I looked at the clock, we had 17 seconds. I thought we had time left to throw one underneath and kill the clock. Unfortunately the clock was down to 7 when I looked back up after the completion. That wasn't enough time to get the spike.
"That's my mistake that happened. We needed points, at least 3, and definitely another shot at the end zone, so that was on me. We have to get that."
It was an ugly visit to Atlanta for the Saints, from start to finish.
When the Saints arrived in Atlanta, their bus was pelted by eggs at the airport.
Michael Turner scored on Atlanta's opening possession, Tony Gonzalez hauled in a touchdown pass from Matt Ryan, and Matt Bryant booted three field goals, including a 55-yarder.
The defense did the rest. Thomas DeCoud, Sean Weatherspoon and Jonathan Babineaux also had interceptions for Atlanta.
Brees completed 28 of 50 passes for 341 yards.
The Falcons opened the game with a dominant drive.
Ryan completed a pass on the first play from scrimmage and then turned it over to a running game that has struggled most of the season. Turner burst around right end for a 35-yard gain. Jacquizz Rodgers broke off two straight 14-yard gains. Turner scored from 3 yards out for his 58th touchdown in five seasons with the Falcons, breaking the team record he had shared with Terance Mathis.
Atlanta struck again in the opening minute of the second period. Julio Jones hauled in an 18-yard throw from Ryan, setting up a 17-yard touchdown pass to Gonzalez in the back of the end zone. He beat former teammate Curtis Lofton; maybe as a sign of respect, Gonzalez just flipped the ball over the crossbar instead of his customary basketball dunk.
Brees' second interception, this one a sloppy pass behind running Chris Ivory that deflected into the arms of Weatherspoon, set up Bryant's 45-yard field goal for a 17-0 lead.
The Saints took control the rest of the second quarter and most of the third. Ingram's touchdown run capped an 11-play, 80-yard drive. Hartley's first field goal, from 21 yards in the third quarter, ended a 15-play, 83-yard drive.
Hartley connected again from much farther out on the Saints' next possession, a 52-yarder that brought New Orleans even closer.