The Australian midfielder crossed his wrists as though he had been handcuffed and later revealed he was dedicating the goal - Everton's second in a 3-1 win against Portsmouth - to his older brother Sean, who was jailed for six years in January for partially blinding a man.
Saying that he knew some would not "be in favour" of the celebration, he said: "Goal celebrations are a personal matter and up to the player to decide - no-one dictates what the player can do as long as he stays within the laws of the game, as long as it doesn't result in a caution.
"It clearly was a very personal thing for Tim Cahill.
"Anyone who saw the pictures will see he was emotional and it meant a lot to him.
"As long as he keeps getting the opportunity to score goals, that is important.
"Tim is a highly intelligent young man and makes his own decisions and saw fit to send a message to his brother, if that's what he was doing.
"He is a very articulate young man and will have weighed up the pros and cons and decided to do it because it was a personal and emotional matter.
"I am sure Tim was fully aware that some people would not be in favour of what he did before he did it."