The controversial penalty against Brooks came during the fourth quarter and wiped out a sack and fumble, allowing the Saints to retain possession on their way to a 23-20 win.
Brooks later argued that the incident did not merit a flag, describing it as a bear hug, while Brees said he had been the victim of a clothesline tackle.
"I can tell you how I felt when I got hit," Brees told reporters. "It felt like I got my head ripped off. And I get up and I've got a mouth full of blood. So there was no doubt in my mind that, 'Hey, it's gonna be a penalty'."
Brooks said: "I basically bear-hugged him. That's just how football is played. Football, the way they call stuff these days, it's watered down. It ain't real no more."
Dean Blandino, the league's vice president of officiating, defended the call after reviewing the play.
"You can't make forcible contact to the head or the neck area, even if the contact starts below the neck and rises up," Blandino told NFL Network.
"If there's force to that contact, it's a foul. Watch the initial contact, maybe around the shoulder, but it rides up into the neck area and brings the quarterback down with force."
The 8-2 Saints, who lead the standings in the National Football Conference South, are next in action on Thursday, against the Falcons in Atlanta.
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