So he reminded the group last week. He pointed toward a couple of 2010 losses to Arizona and Cleveland. Players also recalled a near-loss to a Carolina team that, like the Jaguars on Sunday, had just handed the keys to a rookie quarterback in his second start.
And yes, New Orleans probably did benefit Sunday because of this. A fast 14-0 start, unlike any of their first three games, proved their awareness to a "trap" game even if they later settled for three field goals without touchdowns down the stretch.
Nothing wrong with learning from history. In fact, there's nothing smarter.
But the Saints still find themselves in some interesting territory these days, worthy of the attention they seem willing to give it as they move forward. As the team tries to develop its identity, it needs to learn from history.
Not try to recreate it.
"Each team is different," Payton said Sunday, when asked about last year's Week 4 struggles against the Panthers compared to this one.
The coach then said this game against Jacksonville reminded him more of a noble Week 3 victory in 2009 when, despite not hitting on all cylinders particularly in the passing, the Saints left Buffalo with a feel-good win because other units stepped up.
It was yet another post-game comment Sunday that shed light on a theme provoked plenty by reporters and fans -- and validated plenty by players and coaches: Everything about the Saints right now centers on comparisons.
Is this as close as the Saints have been to being a balanced offense as they were in 2009? What was the difference between Week 4 this year and Week 4 last year? Is this a better team now at this point than it was in 2010?
"We're just really ironing out the identity of this team," said Colston, doing his best to quell any outside desires to pit this squad against the 2009 version.
Of course, there's nothing wrong with wanting to muster up the type of mojo that New Orleans possessed two years ago, while avoiding repeating problems that kept the team from doing just that in 2010.
The Saints seemed to accomplish this to a degree worthy of praise with the overhaul of their running game this offseason.
"It's probably the best group that I've been around," Brees said. "All three guys on this team have a significant role. That adds more weight to what these guys do."
Yes, Brees remembers that he played on a Chargers squad with LaDainian Tomlinson, Michael Turner and Sproles. But Tomlinson handled the bulk of the carries on that team, which caused Brees to explain that New Orleans' unit is a unique, well-rounded group that provides greater versatility.
Case in point: The Saints rushed for a season-high 177 yards Sunday. Sproles had 75 yards. Ingram had 55. Thomas had 36. All contributed.
"For us to get that many rushing yards, and to throw the ball the way we did (Brees finished 31 of 44 with 351 yards), I'm very happy," tackle Jermon Bushrod said. "But we left a lot of points out there."
And that's OK. It's OK because the Saints took a very legitimate step Sunday, even during a boring game, toward developing the identity that will define this group. And what exactly might that identity be shaping up to be?
"You know what, at the end of the day, when it was our turn to go up there and put points on the board, we did that," Bushrod said. "And when it was the defense's turn to go out there and hold them, they did that."
Obviously, the Saints will establish themselves in a much more defined way as the rest of the season plays out. But based on the first four games, this group looks capable of many types of wins: Coming from behind. Starting fast. Throwing when necessary. Running if it works.
And of course, they'll surely continue to attack with a risk-taking offense, a bold coach and one of the best quarterbacks in the league. As long as Payton and Brees are around, that's not going to change. Nor should it.
Each team is different. Now, it's time to treat them that way.
"I think this is a good team," defensive end Will Smith said. "We have a good feel for it. You never know, and you can say that every year. But I think just the guys here, everyone is confident in everyone else's ability. Now, we'll start to build on that."