With Atlanta suffering a loss at Cleveland Sunday, the Saints had a chance to be in the Super Bowl derby with a win over the Panthers (7-9).
But New Orleans (9-7) dropped their third straight game, managing only a pair of field goals in front of a disapproving Superdome crowd.
Last year, the Saints dropped their final four games to finish at 7-9.
"It hurts more than last year because I know that we are a better team," said wideout Joe Horn, who was involved in a pregame fight. "We had better guys. We were more focused this year."
Cousin recovered a fumble in the first quarter, picked off Aaron Brooks in the second and sealed the win with another interception in the closing seconds.
Booed throughout, Brooks was 12 of 31 for 145 yards as the Saints failed to move the ball against one of the best defenses in the conference.
"We gave it everything we had," Pro Bowl returner Michael Lewis said. "Everybody left everything out on the field. We just couldn't execute."
The Panthers were not much better, but Rodney Peete threw a 15-yard touchdown pass to fullback Brad Hoover late in the second quarter to account for all the points Carolina needed.
"That's character," wideout Mushin Muhammad said. "I've been talking about that the whole season. This team has more character and more togetherness and has gelled so tightly that it's almost an eerie feeling."
New Orleans' setback gave the Atlanta Falcons (9-6-1), losers in Cleveland on Sunday, the final wild card berth in the NFC.
The Saints came up with their worst game of the season at the wrong time. They began the day with an NFC-high 426 points but totaled only 244 yards of total offense against the fourth-rated defense in the conference.
New Orleans punted on three of its first four possessions after producing a field goal that opened the scoring, then coughed up the ball on consecutive drives.
Cousin came up with his first takeaway early in the second quarter, halting a long drive when linebacker Mark Fields stripped the ball from Jake Reed following a 16-yard completion.
On New Orleans' next possession, Brooks threw high to rookie Donte' Stallworth, who tipped the ball into the hands of Cousin.
The play resulted in a chorus of boos for Brooks, a common occurence Sunday.
"When you play at home, most crowds try to back you and help you win," Haslett said. "That's what home-field advantage is all about. I guess it is different here and I don't understand it."
The Panthers had only 273 yards of total offense but went 45 yards in seven plays on their final possession of the first half, taking the lead for good on Hoover's touchdown catch.
It marked the 11th time this season Carolina scored 14 points or fewer.
"Trust me, I'll take 40 anytime we can do it," Fox said. "I don't want to label my game or our game. My hat is off to our defense. Our defense was tremendous."
The Saints still had a chance to win the game in the closing moments, but Cousin slid in front of a third-down pass near the right sideline to cap a career day.
"He had a great game," Fox said. "He's had a good season for us. He's been very steady. He's a leader in the locker room. He's a tenacious competitor."
After a review, officials upheld the interception, which sealed the Panthers' perfect day as spoilers.
"That's just part of it," said Fox, whose team went 1-5 against NFC South opponents. "That wasn't our motivation. Our motivation was to play good against a playoff-caliber team at their home against a division opponent."
Moments after Cousins' second interception, the Browns (9-7) held on for a 24-16 win over the Falcons -- a result that could have gotten the Saints into the playoffs.
"We weren't worried about that," Haslett said. "We were trying to win this game."