The 41-year-old spent a year on the south coast in charge of the Seagulls and although he led them to the play-offs, the Spaniard resigned from his position on Monday
The Seagulls fell to a heavy 4-1 defeat in the second leg at the iPro Stadium resulting in a 6-2 aggregate loss and prompting the resignation of 41-year-old Garcia.
The Spaniard had been in charge of Brighton for a season, taking over from Gus Poyet in June 2013 following a spell at Maccabi Tel Aviv.
A statement from Garcia on club's official site read: “The club has been aware of my thoughts for several weeks and during this time I have had discussions with both the chairman, Tony Bloom, and chief executive, Paul Barber. I have enjoyed my time with the club but, although I do not have any immediate plans, I have decided to move on.
“I’m very proud of this season with Brighton. The Championship is a very difficult and competitive league but our record this season has been very good. I wish Brighton every success for the future."
A mixed campaign saw Brighton sneak into the play-offs with a last minute goal downing Nottingham Forest 2-1 but the Championship side - who finished fourth last year - could not carry that momentum past Steve McClaren's Rams.
However, chairman Tony Bloom paid tribute to Garcia, adding: "We are extremely grateful to Oscar for his efforts this past year, and for providing us with another exciting and memorable season at the club."
Chief executive Paul Barber added, “On behalf of the club, I would like to thank Oscar for his efforts and to wish him all the very best for the future. The chairman and the board will now begin the search for Oscar’s successor."