Cutler, who was featuring for the first time since recovering from a groin injury, hurt his left ankle during the second quarter of the game but played on until he was finally taken off in favour of Josh McCown on the Bears' final drive.
McCown threw a late touchdown pass for the Bears, but a failed two-point conversion attempt condemned them to a 21-19 defeat at the hands of their NFC North rivals.
"I didn't want to take [Cutler] out unless he felt he couldn't do the job. It was, I thought, a very courageous performance throughout," Trestman told The AP.
"Then at the end I took him out because I knew he would have to run around in the two-minute drill and that's when we decided to put Josh in the game."
The defeat leaves the Bears tied for second place in the NFC North, level with the Green Bay Packers and one win behind the Lions.