Coppell, who had been at the helm of the Madejski Stadium outfit for five-and-a-half years, ended his reign in the wake of the 2-0 second-leg defeat which saw the Royals lose 3-0 on aggregate.
Coppel, 53, refused to comment on his future in the post-match interview, but released a statement via the club's official website shortly after confirming his departure.
"Following our exit from the play-offs, I feel it's the best thing, for both the club and myself, for me to leave," he said.
"I have thoroughly enjoyed my time as Reading manager and would like to thank everyone connected to the club for the support I have received."
Coppell took charge of the Berkshire club in 2003 and guided them to the Premier League for the first time in their history before relegation at the end of the 2006/07 season.