The official is accused of making "inappropriate comments" interpreted as being racist in nature towards John Obi Mikel during Chelsea's 3-2 defeat to Manchester United last month.
Clattenburg has strenuously denied the accusations and the Metropolitan Police closed their investigation into the matter, prompted by a complaint from the Society of Black Lawyers, on Tuesday.
The Football Association is due to complete its own probe on Friday but by then it will be three weeks since the match was played and Cech says he is also keen for the matter to be resolved quickly.
"I think there should be better communication from the side of the referee towards the public as well," he said. "I think it would help.
"The players come and say fair enough I made mistake, it was completely wrong, I shouldn't have dived, I shouldn't have done this, and you get the credit for that.
"And I think you'll get respect from the people and I think this is what can sometimes happen with the referees. Their job is very hard anyway and we all know that but I think the communication could be better."
On the case against Clattenburg, he added: "For me it is difficult to comment on something that I didn't hear or was not even involved or even close.
"I believe that if you come with something like that, you need to have a really good case to say it because if not it would waste time of everybody and again it wouldn't be good for football.
"If there was a case it is not because Chelsea want to do something, it is just because there is a case and again, I hope that this story will be finished as soon as possible."