Unai Emery says he wishes he could have achieved “better results” for Arsenal, after being sacked by the Premier League club on Friday.
The 48-year-old, who replaced Arsene Wenger in May 2018, lost his job after their longest winless run for 27 years.
Arsenal are eighth in the Premier League, eight points off the top four.
“Not a single day has gone by without me stopping to think about how lucky I have been to work for this club,” Emery said in a letter to Arsenal fans.
Arsenal said the decision to sack Emery had been “taken due to results and performances not being at the level required”.
The Gunners lost 2-1 at home to German side Eintracht Frankfurt in the Europa League on Thursday.
Their seven-game run is their worst without a victory since February 1992, when they were winless in eight games under George Graham.
“It has been an honour to be the Arsenal head coach,” said Spaniard Emery, who previously led Paris St-Germain to the French league title and won three Europa Leagues with Sevilla.
“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 would have liked nothing more than to have achieved better results for you.”
Arsenal finished fifth in Emery’s first season in charge at Emirates Stadium after he replaced the long-serving Wenger.
The Gunners spent more than £130m in the summer after signing winger Nicolas Pepe, centre-back David Luiz, left-back Kieran Tierney, striker Gabriel Martinelli and defender William Saliba, who will join next summer, while also bringing in midfielder Dani Ceballos on loan from Real Madrid.
After losing just one of their opening 11 matches, their form dipped and led to Emery facing increasing criticism and pressure.
Arsenal’s last Premier League victory was a 1-0 win over Bournemouth.
On Saturday, they were fortunate to secure a 2-2 draw – their sixth of the season – at home to Southampton, with Alexandre Lacazette scoring an injury-time equaliser.
“It has been a year and a half full of emotions, of great moments and some other more bitter ones,” added Emery.
“I want to tell all of you that I have worked with passion, with commitment and with effort.”