Carril -- who is widely known for executing the "Princeton offense," which he used throughout the majority of his career -- died "peacefully," the family said.

The Hall of Fame inductee coached the Tigers for 29 years ... racking up 514 wins, 13 conference championships and 11 NCAA Tournament appearances.

Carril served as a public information officer in the U.S. Army before kickstarting his coaching career at the high school level. He became head coach at Lehigh University in 1966, where he remained for one season before taking the Princeton job.

Coach went on to join the Sacramento Kings as an assistant for several seasons.

Legendary commentator Dick Vitale -- who was good friends with Carril -- tweeted about the loss ... saying, "I believe that in defining greatness in coaches u must determine if they get maximum out of their TEAM personnel," he tweeted.

"PETE CARRIL is a prime example of a brilliant coaching mind that got max out of his talent."