"It has been a year and a half full of emotions, of great moments and some other more bitter ones," Emery said
Unai Emery said it had been an "honour" to coach Arsenal despite being sacked as manager of the Premier League club on Friday after just 18 months in charge.
The 48-year-old Spaniard was fired following the 2-1 home defeat to Eintracht Frankfurt in Thursday's Europa League match, which extended their winless run to seven games.
Assistant Freddie Ljungberg has taken over as interim manager with ex-Juventus coach Massimiliano Allegri and Wolves boss Nuno Espirito Santo among the early favourites to be named the next full-time boss.
Despite his sacking, Emery insisted it had been an "honour" to manage the London giants.
"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."
Former Arsenal player Ljungberg said he would work hard to improve the atmosphere at Arsenal.
"However long I oversee @Arsenal I will give everything I have to put smiles on faces again," he tweeted. "We have a busy few weeks ahead and the team needs your support. Let's get to work!"
Arsenal are on their worst run without a victory since 1992, when they went eight games without a win under George Graham.
They are already eight points off the top four after failing to win a Premier League match since October 6.
Emery was appointed as successor to Arsene Wenger in May 2018 after a trophy-laden career at Sevilla and Paris Saint-Germain with a brief to make Arsenal a Premier League force again.
The club, who have not won the Premier League since 2004, had stagnated in the final years of Wenger's 22-year reign despite a series of cup triumphs.
But Arsenal could only finish fifth last season, missing out on the riches of the Champions League for a third straight year.
Emery spent more than £130 million ($168 million) in the close-season, bringing in a clutch of players including winger Nicolas Pepe, centre-back David Luiz and left-back Kieran Tierney.
But despite the reinforcements they have collected just 18 points from 13 games so far this season.
Emery has had many off-field issues to contend with, losing Aaron Ramsey on a free transfer to Juventus at the end of last season.
He then saw former captain Laurent Koscielny refuse to travel on a pre-season tour to the United States as he pushed through a move away from north London.
Granit Xhaka was named as his successor but he was stripped of the captaincy after swearing at supporters who jeered him following his substitution in a 2-2 draw with Crystal Palace last month.
There was also upheaval behind the scenes as two of the men who made the decision to appoint Emery, chief executive Ivan Gazidis and head of recruitment Sven Mislintat, departed within nine months.
And the attempted carjacking of Mesut Ozil and Sead Kolasinac on the eve of the new season played a role in unsettling the squad.
Emery is the third Premier League manager to lose his job this season after the dismissals of Watford's Javi Gracia and Tottenham's Mauricio Pochettino.
The Arsenal Supporters' Trust issued a statement saying the club needed to change more than its manager.
"Emery's departure is the easy part," it said. "The more difficult challenge is to recruit a suitable successor. We are far from certain that Arsenal has the right personnel to lead this process.
"The AST has long been advocating that the most important changes needed at Arsenal are in the boardroom, where Arsenal need better governance."