He should protect Bevell because throwing a guy under the bus for one bad call would be a bad move for the organisation, and as head coach he is responsible to do right by the team.
NFL coaches are very cognizant of the fact that they do not make good decisions in the heat of the moment. If you look up how Bill Walsh used to plan, he did it so that pretty much none of his decision making was done on the day of the game. He would have a script of 15-30 plays for normal situations, then scripts for backed up offense, 3rd and 3 offense, 3rd and short, 3rd and long, red zone, 20 yard line first down (a lot of shots to the end zone). You could also add in special 2nd and 1 plays because that is a prime moment for taking big shots. Modern teams probably have a 2 minute script and a 4 minute script too. So most of the play calling was actually done by Thursday in game week and the only decisions he had to make on the fly were minor adjustments. The point I'm making is, that special situation that was impossible to prepare for is not what should define Bevell's career, and certainly not his status with the Hawks.