Shula, the Hall of Fame coach who guided the Dolphins to back-to-back Super Bowl wins in the 1970s, recently told the Miami Herald that he is hurt by the saga that has become a national controversy.
Incognito played all 16 games in 2012 and was eventually voted onto Miami's leadership counsel by his teammates in 2013.
"You win with good people on and off the field," the 83-year-old Shula told the Herald. "They took a chance on a guy with a bad reputation, and it backfired on them."
The NFL is investigating the troubled relationship between Incognito and teammate Jonathan Martin, who left the Dolphins last week because of emotional issues stemming from alleged harassment and misconduct.
Incognito was suspended last Sunday for conduct detrimental for the team after being identified as one of multiple teammates who harassed Martin, who will discuss the case late next week with a special investigator hired by the NFL. Allegations by the second-year offensive tackle include a malicious physical attack by a teammate.
"It hurts," Shula told the Herald. "You hate to see it happening."
Several Dolphins players refuted Martin's claim of the physical attack, saying Saturday that they were unaware of any violence in the locker room.
Incognito has long been known for out-of-bounds behavior, including a May 2012 incident that surfaced this week. A police report said a female volunteer at a Dolphins charity golf tournament complained that Incognito harassed and molested her.
Dolphins coach Joe Philbin said Saturday that the team was aware of the 2012 incident and "took immediate action," declining to reveal specifics.
Shula is the winningest coach in NFL history and posted a 328-156-6 career record in 33 seasons -- 26 with the Dolphins. He coached Miami to the only undefeated season in league history in 1972, when the Dolphins won Super Bowl VII to complete a 14-0 season.
The Dolphins also won the Super Bowl the following year under Shula, who told the Herald that he wants to see the franchise "get back that credibility."
Information from ESPN.com Dolphins reporter James Walker and The Associated Press was used in this report.