Roberto d'Aversa said he would "forever be grateful" to Parma despite being sacked on Sunday by the side who he led from the third division back into Serie A.
Italian media reported he would likely be replaced by former Lecce boss Fabio Liverani.
"To those who applauded, supported, jeered and criticised, especially the latter, I thank you. Without their push, their motivation to keep doing better, we wouldn't have come this far," he said in an open letter.
"Arrivederci Parma, I will forever be grateful to you,"
Parma said D'Aversa's sacking was "a result of the fact that over the last few weeks, the cohesion, unity of intent, harmony and mutual enthusiasm which have been so key to the successes achieved together over the last few years have disappeared".
Parma were relegated into the fourth division in 2015 after being declared bankrupt.
D'Aversa took over with the team in Serie C, overseeing promotion to Serie B in 2017 and Serie A a year later.
The club finished 11th last season after being 14th in their first campaign back among the Italian elite.
"Nothing can erase the unforgettable achievements engraved into the club's history thanks to the coach and his coaching team's fundamental contribution," Parma said of D'Aversa.
"The club expresses its gratitude for everything over these past few years, wishing Roberto the best of luck for the next step in his career."