The Jets scored two rushing touchdowns and four field goals on the way to victory, with former Saints running back Chris Ivory having a particularly productive day, making 139 yards and scoring one of the touchdowns.
Vilma was full of praise for the Jets after the match and believes that they were the better team on the day.
"They did a really good job scheming us and figuring out how to get those runs on us, how to get Ivory the ball and get some positive plays on us," Vilma told The AP.
"They did a very good job and deserved to win this game. Ivory got the ball and had 9 or 10 yards before someone touches him."
Despite the defeat, the Saints still sit top of the NFC South, one win clear of the Carolina Panthers in second.