The FA concluded an investigation into the incident in the game between the Blues and Manchester United on 28 October by declaring the 37-year-old had "no case to answer."
"Mark's delighted that his innocence has been proven after all this time," Leighton told Sky Sports News.
"It was right that the FA considered fully and investigated fully the issues so that there was no doubt that he was innocent.
"I think there are some lessons to be learnt - Mark is clearly very upset that his reputation has been dragged through the mud by the process. There was no need for Chelsea to make it publicly aware that this allegation had been made.
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And former referee Dermot Gallagher is confident "a line has been drawn in the sand", and believes every referee will be "very, very happy" at the findings before hailing Clattenburg for the way he has dealt with the whole affair.
"I think what's he's done is kept himself to himself and carried on training. He's been involved with the PGA, he's kept his dignity but more importantly he's kept a thoroughly professional outlook."