One could make an argument for firing Martinez, Parra, Gutierrez, and Bob Carpenter all for incomptence based on what happened in the bottom of the 9th. I feel bad for Carpenter because this is his final year regardless. Why wait until the end of the year to get rid of the others?
When your young players are boneheads, which is the case here, the coaches and manager must give explicit instructions on what to do in any situation. It's better to have no coaching at all than incompetent coaching.