However, even though another loss would see the Jets fall three wins behind the Patriots, Ryan does not believe that all of their chances hang on Sunday's match.
"'Must-win' might be a little much right now, even for my deal. I'm notorious for throwing those bad boys out," Ryan told reporters.
The Patriots picked up their fifth victory of the season in dramatic fashion as quarterback Tom Brady threw a match-winning touchdown pass with five seconds on the clock against the New Orleans Saints.
Ryan's brother Rob is the defensive coordinator for the Saints, and Rex admits that Brady's last-gasp heroics hurt him as much as they did his brother.
"It was a horrible day for the Ryan family. It's a good thing my dad is out of coaching. It was tough," Ryan added.
"Heck, yeah, you want to see them lose, no question. You want every team in your division to lose, in particular New England."
The Jets have already played the Patriots once this season, losing 13-10 on September 12.