It wasn’t long after 49ers kicker Phil Dawson booted the overtime field goal that handed the Saints their fifth defeat of the season last week that virtually everyone began drawing similarities between San Francisco and New Orleans’ next opponent, Cincinnati.

The Bengals (5-3-1) head into Sunday’s visit to the Mercedes-Benz Superdome coming off a disappointing 24-3 home loss to Cleveland. Since a week earlier the 49ers had dropped in on the Saints (4-5) after having lost unexpectedly to St. Louis, observers began questioning whether New Orleans could survive another team that had prepared itself desperately to bounce back from a bitter setback.

Not surprisingly, when discussing the topic this week, the Saints said they do indeed believe they can upend the Bengals. But that’s not because Cincinnati quarterback Andy Dalton has thrown more interceptions (nine) than touchdowns (eight), or because the Bengals defense has allowed the third-most total yards and second-most rushing yards in the NFL. It’s not because the Saints’ record at the Superdome the past three seasons Sean Payton has coached them remains an excellent 20-1, blemished only by the loss to San Francisco.

It’s because the Saints have promptly followed two of their losses this season with wins by a combined score of 57-40. They then followed a third loss this campaign — one of four they’ve had by a margin of three points or fewer — with a pair of victories by a combined score of 72-33.

And it’s that trait that has helped the Saints take advantage of a weak NFC South and cling to a lead in the division, ahead of Carolina (3-6-1), Atlanta (3-6) and Tampa Bay (1-8) in the race to secure hosting privileges for at least one playoff game.

It’s that ability to rebound — more than the Bengals’ shortcomings — that explains the Saints’ stiff upper lips this week.

“It tells you about the resolve that we have: We’re not going to lay down, no matter what,” said Ben Grubbs, the two-time Pro Bowler manning the Saints’ left guard spot. “We’re going to keep fighting. As a man, you’ve got to understand that we take care of our responsibility — no matter what the outside circumstances are, I try to focus on what I have to do, and I’m positive the guys in this locker room do the same.”

Saints players denied they’ve amped up the urgency level after losses. They insist they’ve been as attentive and zealous gearing up for the games they lost as the contests they won.

The difference has come during the games themselves — being on the positive end of the crucial plays only in the games they’ve pulled out. The negative moments that stand out are a 28-yard reception surrendered to set up a late, game-winning field goal at Cleveland; the 73-yard touchdown reception given up on third-and-long that helped turn a 13-point deficit at Detroit into a one-point loss; and lost fumbles in overtime that led to game-winning field goals for Atlanta and San Francisco.

“We haven’t come through, obviously,” Saints defensive coordinator Rob Ryan said. “We know we ... are going to be in every game. We just have to finish and execute.”

“Things happen,” linebacker Parys Haralson said. “Sometimes the ball bounces your way, and sometimes it doesn’t.”

But perhaps unlike the one-, two-, three- or no-win teams out there that have sustained lengthier losing streaks this year, the Saints have had both the adequate will and talent to post at least one victory in the wake of each defeat they’ve suffered after an 0-2 start to the campaign, Haralson added.

“Nobody gives up,” he said, “(even if) we’ve had half the season we’ve wanted to right now.”

And if you talk to second-year Saints left tackle Terron Armstead, it would not be smart to bet that would change now, even if Cincinnati will be scrapping to rectify the blowout they were subjected to when they last took the field on game day.

“We know what we have in the locker room,” Armstead said. “And that’s relentless guys that keep fighting.”