The Cowboys gave the ball away six times during their pre-season match against the Arizona Cardinals, prompting the coaching staff to stress the importance of ball retention in training last week.
However, during a pre-season match on Saturday, DeMarco Murray fumbled the ball and Garrett immediately hauled the running back off as a message that such mistakes are unacceptable for his side.
Murray admitted to being frustrated at the decision, but insisted that he respects it and Garrett believes that he understood the reasons behind it too.
"[The fumble] can't happen. I don't care who you are; we can't have it," Garrett told reporters.
"DeMarco's a man. He understands team. He understands what his role is on this football team. We just felt that was the right thing to do, and he responded exactly how we thought he would respond, came back and played really hard and really well and took care of the rock."
The Cowboys will face the Houston Texans in their final warm-up game on Thursday before getting their regular season underway at home to the New York Giants.