It is unproductive for a coach to criticize an athlete in the presence of others, yet it happens quite often. This can have a more damaging effect on team unity if done in a public setting say, after a game in view of all the spectators. Punishing the team for the mistakes of a few can only lead to division, certainly not unity. Besides, most coaches I know have made a few mistakes themselves. It is a part of life. But, how we handle our players mistakes is what defines our character and eventually our reputation.
The handling of mistakes should be done one on one and away from the public eye. Say, on the practice field the next day. This gives time for all parties to think more rationally about the degree of the mistake. Especially in the light of the following:
1) All players make mistakes. So, Expect mistakes.
2) Players don't intend to make mistakes.
3) Players don't like to make mistakes.
4) Players want to "make up" for mistakes made.
5) Players want to learn from their mistakes.
6) Players are hurt more by self-regarding feelings than criticism from others when they make mistakes.
So remember this before punishing the team for the mistakes of a few. All the running of bases after a game will not change the fact the majority of your team did not make the mistake. But it can change the majority of the team's view of their coach.