As promised, Victory Monday didn't morph into Deception Monday for the New Orleans Saints.

A historic 27-26 victory over the Falcons in the season opener at Mercedes-Benz Stadium in Atlanta – with the Saints completing a 16-point comeback in the fourth quarter, the largest deficit a New Orleans team ever has overcome in the fourth – remained pulsating. But not so much that it masked the reasons the Saints were required to rally.

"We've got a good group of guys that understand how to win in our league, but also know what keeps you from winning in our league," Coach Dennis Allen said Monday. "And they know that we did a lot of things in that game that could have kept us from winning that game. But fortunately, we were able to make enough plays to win it.

"But our guys know that that won't be good enough moving forward."

The sore spots were a slow-starting offense – 104 yards in the first half, including minus-2 passing – and a prideful defense that allowed 201 rushing yards and two touchdowns on 38 carries.

New Orleans was able to correct each phase in the fourth quarter, with the offense producing 17 points and quarterback Jameis Winston completing 13 of 16 passes for 213 yards and two touchdowns, and the defense limiting Atlanta to a field goal while forcing two punts.

"There's a ton of stuff that needs to be corrected," Allen said. "But I would say this, it's been my experience over the last however many years, you get into these games like this and the good teams are able to win these games when they're not playing at their best.

"I credit Atlanta. I thought they had a really good plan, I thought they played hard. They made some things really difficult and challenging for us, but at the end of the day we made enough plays to win the game. I was proud of the way they fought and competed, but we also know we've got a lot of stuff that we've got to clean up."

Allen said the passing game was able to get on track after ironing out some mistakes.

"I thought the pass protection was actually pretty solid overall," he said. "We had a couple of miscues in terms of identifying on the protection, and there was a couple of plays where maybe we were a little deep in the pocket, maybe we held on to it a little bit.

"Here's the thing: When you talk about pass protection, there's a ton of different variables that go into it and typically the first thing, everybody starts to talk about the offensive line and things of that nature. But there's a lot of different elements that are involved in that – receivers running the proper route at the right depth, the quarterback getting to the right depth (and) getting rid of the ball, backs in protection. So there's a lot of different things that are involved in that.

"I don't think we were as clean as we needed to be early in the game, particularly in the first half. But I felt like as the game went on, I thought we got a little bit better."

Getting into a hurry-up offense in the fourth quarter helped, he said.

"We got into a little bit of a two-minute type of operation and opened it up with a completion to (tight end) Juwan (Johnson), and I thought we just kind of got into a little bit of a rhythm there in terms of throwing the ball. I thought Jameis felt real comfortable in that situation.

"I think when you get into those two-minute type of deals sometimes it can kind of calm the look down of the defense a little bit, and I felt like that was a little bit of the case there. But we got into a rhythm and I think once Jameis got into a rhythm, he felt good about what he was doing."

Allen said the Saints' run defense simply was "unacceptable."

"That's not been the standard that we've had around here and it won't be the standard that we'll have around here," he said. "I don't think I was as good as I needed to be in helping our guys out.

"I do think that there's a little bit of an element of surprise in terms of exactly what are they going to do with a new quarterback. And look, they blocked us. We have to coach better in that area and we have to play better in that area."

Linebacker Pete Werner agreed that the defense will have to improve.

"We did finish the way that we like to, with a win," said Werner, who had a forced fumble and a tackle for loss against Atlanta, along with 13 tackles. "But you can talk to any defensive player on this team, any defensive coach, we're not satisfied with that. The amount of yards they put on the ground, that's unacceptable.

"We're fortunate for the win. But as a defense, feeling vibe from the players and coaches, we can't have a performance like that again."