Di Montezemolo announced in September that he was stepping down from his role after a 23-year spell at the helm of the Maranello-based squad.
Ferrari endured a poor season during 2014, failing to win a race for the first time since 1993, and finishing on the podium just twice.
New chairman Sergio Marchionne said earlier this week that Ferrari was paying for the mistakes it had made in recent years, and blamed strategic decisions "made by others" for having started work on next year's car late.
Formula 1
Aston Martin want Vettel to stay and expect answer 'imminently'
14/09/2021 AT 08:45
Di Montezemolo responded to Marchionne in the Italian media, suggesting he deserved more respect for his work during the years.
"I did not intend to fuel this argument, for the deep love I have for Ferrari, for the respect deserved by those who work there now and who had worked and won there in the markets and on the circuits," di Montezemolo told the ANSA news agency.
"These past weeks, however, I have heard reiterated, gratuitous, and sometimes unfounded accusations. I don't want to fall for such provocations.
"The sporting successes, more numerous than those gained by any other team, the strength and prestige the brand has built in the world, and the financial results that have been fundamental for the FCA group and that this year are the best in the history of the company, speak for themselves.
"I trust that Christmas will calm down spirits and bring better judgement."
Last week, di Montezemolo was reappointed as a non-executive director of the Formula One Group, in a similar role to the one he held during his stint as Ferrari boss.
Marchionne said he did not agree with the decision.
"The CEO is once again [Bernie] Ecclestone, but if we were asked for an opinion on Montezemolo we would have said no for a matter of good taste," Marchionne was quoted as saying by Gazzetta dello Sport.
"In respect for the others, you can't push for an ex-president of yours for such a role.
"You can't do certain things for a matter of governance.
"And myself, as head of Ferrari, had I been around back then I would have said no regarding [Jean] Todt at the helm of FIA, despite his merits and capabilities."
Translation by Michele Lostia
Formula 1
Verstappen's collision with Hamilton a 'tactical foul' - Wolff
13/09/2021 AT 08:46
Italian Grand Prix
'I feel very, very fortunate' - Hamilton says halo saved him in crash with Verstappen
12/09/2021 AT 19:52