Garcia penned an open letter to the club's supporters after the 4-1 loss to Derby on Sunday completed a 6-2 aggregate defeat in the play-off semi-final.
His resignation comes just 11 months after he was appointed manager.
I would like to thank the Brighton & Hove Albion fans for their tremendous support throughout the past year. I have been proud to be the head coach of your club.
Yesterday, we gave it our best. We didn’t have the best of luck, but regardless we were simply beaten by the better team. Overall, when all things are considered, particularly our terrible luck with injuries both yesterday and since the very start of the season, I think it has been an excellent year for the club.
The Championship is undoubtedly one of the most challenging leagues in the world. It is highly competitive and it is made up of a wide range of clubs with very different budgets. Parachute payments for eight of the clubs in the league and new Financial Fair Play rules make it even harder. Despite these issues, I feel we have performed well.
As such, I am incredibly proud of the players - they have given everything for me, the club, and you, our fans. I have also been pleased to have been able to help a number of the club's young players develop and progress into the first team, and I hope they will play many, many games for Brighton & Hove Albion in the future.
I would also like to thank staff at the club. The club has a tremendous group of people at all levels – both at the training ground and in the stadium, who care passionately about the Albion and who are desperate for the club to succeed and to progress further. They too have made me very proud.
Finally, I would like to thank Tony Bloom for giving me this opportunity; and especially Paul Barber, for his support; I have enjoyed a close working relationship with Paul during my time in Brighton.
I have enjoyed my first experience of English football, and I would like to wish Brighton & Hove Albion and the fans of the club the very best for the future. The club will always have a place in my heart and I hope very soon they will be competing at the top level in English football.
The club said in a statement on their official website: "Brighton and Hove Albion have accepted the resignation of head coach Oscar Garcia.
"Oscar met with the club earlier today, to formally offer his resignation to the board, which has been accepted. He has also informed the club's players of his decision."
- Sports & Recreation
- Brighton & Hove Albion