Acknowledging the mistake and apologizing is more positive than you think. This action will help correct a mistake and it will help the referee to move forward without resentment. Nobody is perfect. We all make mistakes.
A sincere apology makes it possible to maintain good relationships on the field. It is known that for referees it is not an easy task to apologize, because most assume that if they do, they will lose their authority.
However, experience shows that it is much more beneficial and productive to take responsibility for mistakes and admit them to the players.
Sorry......I made a mistake !
Apologizing is a skill that does not always mean that the referee is wrong and the player is right. To the contrary, it means that the referee values more his relationship with the players and fans than his own ego. This gesture reinforces his leadership and honesty. That is why it is necessary for the referee to recognize he's wrong in a sincere way. From the fact of being human, we are in the position that anyone can make a mistake.
The credibility of the referees and the quality of their relationships and fair treatment, then become the main factors of loyalty for the real professionals in the match. This also implies empathy toward understanding how a hasty or wrong decision affects a team or players. This is a turning point from which the referee agrees to not to refrain from. An apology begins with one step, that of self-criticism, reflecting upon what is being done and what has caused the error or mistake.
How to apologize
The era of the infallible, ego centric referee is gone. Today professionals are required to assume the possibility of a mistake and be able to apologize when it happens. Of course, considering that in a game this action occurs two or three times, while if it is more than that, it is necessary to review the decisions being made. Do not forget that the apology is attached to a promise of a change in attitude and a solution to the situation created. In other words to show that it will not happen again.
The apology should come from me, never from you. "Sorry to make you feel bad for my mistake." "I have erred in this decision." "I made a mistake." In this way we eliminate any hint of attack that can be felt by the players if we try to justify our own attitude based on their reaction. The phrase "I was wrong, you're right" has an enormous capacity to release tension. These are magic words that encourage the player to accept the apology and automatically recognize your part in the mistake.
Source: Jose Borda , Revista Arbitros