Mertens' deal expired this summer but there was some hope that he could be convinced to stay on for another year.
That hope has now been extinguished after Mertens turned down several new propositions by the Napoli hierarchy.
Mertens joined Napoli from PSV Eindhoven in the summer of 2013 and leaves Naples as the club's all-time top scorer with 148 goals.
His tally of 397 matches puts him fifth on Napoli's all-time appearances list.
Speaking to Radio Kiss Kiss about about the Belgium international's situation, De Laurentiis said: "I feel the love for the club, but I must never forget that football is also an industry as well as pure passion."
"Unfortunately, that means sometimes going against what the fans want.
"When a supporter asks me, 'why don't you keep Mertens?' I can only reply that he offered himself to us for another year, because he knows that he's 35 and then has to retire.
"If he makes it a matter of cold, hard cash, then I have to say no. If I have to pay a disproportionate salary to Mertens, that would take money away from next season's budget."
"I presented him with €4million per season gross and he refused.
"So I said thank you very much to you, your son Ciro, your wife, for everything you've done here and the extraordinary goals scored, but we cannot go beyond our capabilities.
"I need to have money to buy young players who can represent Napoli in future seasons.
"When we changed all the older players to bring in those like Mertens and Koulibaly, the fans were doubtful, but they became champions here."
Napoli, who finished 3rd in Serie A last season, have also lost the likes of Kalidou Koulibaly, David Ospina, Lorenzo Insigne and Arkadiusz Milik this summer.
