Ecclestone, 82, was critical of the controversy generated after Ferrari decided to write to the FIA asking for clarification on Sebastian Vettel's pass on Jean-Eric Vergne during the season finale in Brazil.
Ecclestone said last week that Ferrari was too late to consider a protest, and labelled the situation a "complete joke".
"In the rules and regs normally you have to protest. They [Ferrari] missed that time," Ecclestone told the Telegraph.
"It's a complete joke. What they are saying in that letter is wrong. I don't think there needs to be any action taken. It's completely and utterly wrong."
Di Montezemolo, speaking during the Ferrari World Finals, was critical of Ecclestone, saying "old age" is often "incompatible with certain roles and responsibilities."
Di Montezemolo's comments on Ecclestone came after the Italian criticised the current lack of testing for younger drivers.
"We are constructors, not sponsors: I'm no longer happy that we can't do testing on tarmac and that you can't give any chance for young drivers to emerge," he said.
"Since some people have used the expression 'It's a joke' in recent days, I would like to say that this is the real 'joke'.
"Yes, I'm referring to one of Ecclestone's phrases: my father always taught me that you have to have respect your elders, above all when they reach the point that they can no longer control their words. So I will stop there.
"Certainly, old age is often incompatible with certain roles and responsibilities."