A 3-0 home loss to Udinese in Serie A on Monday proved to be Nicola's final match in charge, with club president Gianni Vrenna having entered the dressing room at half-time.
Nicola led Crotone to a miraculous survival in their first Serie A campaign last season, with six wins from their last nine matches seeing the club turn around a seemingly hopeless situation.
Vrenna said Nicola's decision took Crotone by surprise after failing in an attempt to convince the coach to stay.
"Nobody expected this decision, neither I, neither the team nor the director," Vrenna said. "Between the first and second half of the match against Udinese I entered the locker room to encourage the team and [Nicola] felt that my intervention had delegitimised him.
"It's not in my style, I've never intervened on the technical side, nor on how to deploy the team. I have considered as president who has the right and duty to intervene when things do not go, to go and give a spur to the team.
"The players are witnesses: I just said 'pull out the attributes because we are losing against a team that has only made one shot on goal'.
"This morning we met with Nicola and I tried to tell him to think again, he reiterated his motivations. We accept it and move forward."