Brees threw for five touchdowns during the victory, extending his all-time NFL record to eight career games with five or more touchdown passes in a single match, but he was left unhappy with the number of mistakes that his side made.
The 34-year-old was ultimately pleased with the win, but warned his side that they will not be able to win every game if they continue to make so many errors.
"It's good when you can not play your best and make certain mistakes and still win like we did," Brees told the Associated Press.
"If we continue to repeat these mistakes they will get us beat. That's not good enough for us. We've set the bar high. We have a high standard. We want to be as perfect as we can out there."
The Saints are now top of the NFC South with a 6-1 record ahead of next Sunday's match against the New York Jets.