Emery was dismissed on Friday after the Gunners' winless run extended to seven matches across all competitions with a 2-1 home defeat to Eintracht Frankfurt in the UEFA Europa League.
Pressure had been building on the former Sevilla and Paris Saint-Germain boss, with his tenure lasting a relatively short 18 months.
Emery was quick to pay tribute to Arsenal's fans, board and players in a message posted on the club's official website, despite admitting there had been "bitter" moments during his stay.
Former captain Granit Xhaka clashed with supporters as he was jeered at Emirates Stadium last month, but Emery said the squad "deserve[s] your support".
"It has been an honour to be the Arsenal head coach," Emery wrote. "To all the fans, I want to thank you all from the bottom of my heart for helping me to understand and feel the greatness of Arsenal.
"To all of you who have supported us from every corner of the globe, all of you who have come to the Emirates, all of you who have waited in the rain and cold just to greet me after a game.
"I want to tell all of you that I have worked with passion, with commitment and with effort. I would have liked nothing more than to have achieved better results for you.
"I also want to send a message of gratitude to all Arsenal employees for the way they have treated me. The greatness of Arsenal is in every director, executive, employee, assistant and volunteer.
"In particular, I want to highlight [former chief executive] Ivan Gazidis, who welcomed me to the club, and [head of football] Raul Sanllehi, [technical director] Edu and [managing director] Vinai Venkatesham for their respect, companionship and help.
"Until the very last minute, I have been treated with honour and honesty. And of course, I send my sincere gratitude to the Kroenke family [owners of the club], for their trust."
Emery, who coached Paris Saint-Germain for two seasons prior to joining the Gunners in 2018, has endured a difficult spell in the Premier League.
"It has been a year and a half full of emotions, of great moments and some other more bitter ones," he said. "But not a single day has gone by without me stopping to think about how lucky I have been to work for this club with these players and their professional and personal qualities.
"They have always honoured the shirt they wear. They deserve your support.
"I had already experienced a lot in football, but I have enjoyed and learned a lot in England, in the Premier League, about respect for professionals and about the purity of football."
Former Arsenal star Freddie Ljungberg, who was an assistant to Emery, has taken temporary charge of the Gunners ahead of Monday's (AEDT) meeting with Norwich City.