"Bob is a good football coach and a great person," Kansas City head coach Andy Reid said in a statement. "He played an integral role in the success of our team over the last six seasons.
"I’ve said before that change can be a good thing, for both parties, and I believe that is the case here for the Chiefs and Bob," Reid added. "This was not an easy decision, but one I feel is in the best interest of the Kansas City Chiefs moving forward."
Reid did not say whether Sutton's replacement would be promoted from within his current staff.
The Chiefs were among the worst defenses in the NFL this past season, allowing an average of 405.5 total yards per game -- only the 6-10 Cincinnati Bengals allowed more -- and 26.3 points per game, the ninth-most in the league and the most of any playoff team.
On Sunday, Sutton's defense could not hold a four-point lead on two occasions in the fourth quarter, surrendering touchdown drives of 75 and 65 yards to the Tom Brady-led Patriots. When New England got the ball first to start overtime, Brady led the Patriots offense 75 yards in 13 plays for the winning touchdown by Rex Burkhead. In all, New England gained 524 yards of total offense, including 176 rushing yards.
Even more damning to Sutton was the call by CBS analyst Tony Romo on the TV broadcast. Romo was uncanny in predicting exactly what New England would do, yet the Chiefs were unable to stop it.
"I put this on the defense," Chiefs defensive tackle Chris Jones said afterward. "We've got to build from it, learn from it and we'll be better next year."
"We wanted to do better there," Reid said during his end-of-season news conference Monday. "When it comes down to the last drive, you magnify where it is, but this was the championship game. It was in overtime. When you really cut to the chase of it here, the few games we lost, we lost by minimal points, so we were obviously doing something right."
The 67-year-old Sutton, a former head coach at Army, had been with the Chiefs since 2013. He previously spent 13 seasons with the New York Jets as a linebackers coach, defensive coordinator and assistant head coach.
The Associated Press contributed to this report.