Blackpool’s season ended in farcical circumstances as their final match of the season, at home to Huddersfield, was abandoned after 48 minutes following a fan protest against club chairman Karl Oyston.
The Seasiders finished 21 points adrift of safety.
In a statement issued via the club on Saturday, Clark said: “After a great deal of thought I have come to the decision that it is not in the best interests of either myself or Blackpool FC that I continue as manager of the football club and have therefore tendered my resignation to the chairman, which he has accepted.
“It only remains to thank my staff, the players, the supporters and everybody else involved with the club for their help and support and wish them the best of luck for the future.”
Clark took charge of Blackpool at the end of October, 10 days after he was sacked by Birmingham - who at that stage were one place above the Seasiders at the foot of the Championship table.
The 42-year-old replaced Jose Riga but oversaw only three Blackpool wins in a season punctuated by regular fan protests against the running of the club.
That culminated in a sit-in demonstration on the final day of the season, with supporters pouring on to the pitch in the 48th minute and occupying the centre circle for more than an hour, forcing referee Mick Russell to abandon the match, which had been goalless.
The Football League ruled the match would not be replayed given it had no bearing on promotion of relegation, but is yet to rule on the final result of the match or any further punishments.
The matter is due to be discussed at a meeting on Thursday.
Clark had refused to condemn those who came on to the pitch but the club issued a statement in which they vowed to “work with the relevant authorities to take appropriate action against all those responsible for disorder offences inside the stadium”.
Blackpool, four years removed from the Premier League, are dropping back into the third tier for the first time since 2007.
Clark began his managerial career with Huddersfield, guiding them to third place in 2011 after a club-record 25-game unbeaten run.
They missed out in the play-offs, but in the following season they extended that unbeaten run to 43 regular-season matches, only for Clark to lose his job by February as the Terriers fell off the pace.
Clark returned to management with Birmingham the following June, but struggled to replicate the success he had enjoyed, missing the play-offs in his first season and battling relegation until the final day of the season in his second - ultimately surviving thanks to a stoppage-time goal from Paul Caddis against Bolton.