Patriots won 21 games straight from 2003-2004 (including playoffs) it's the longest streak in modern day football
New England Patriots---The patriots lost their last game in the playoffs
The Buffalo Bills were last in the playoffs during the 1999 season.
The NFL team that holds the record for the longest losing streak are the Tampa Bay Buccaneers. In 1976, they lost every game they played that season. Their record is a 26 game losing streak.
THEE INDIANAPOLIS Colts