Clark, who took over at Victoria Park in the summer, won just three of his nine National League games with the club. The 3-1 loss was a third defeat in a row and a sixth in seven matches, pushing Hartlepool down to 18th in the National League table.
Clark expressed his disappointment at being unable to give the club and its fans something to be proud of, stating: "I resign from my position with immediate effect." He also acknowledged that he had been unable to achieve his goal of getting the team back to where they deserved to be.
Hartlepool United are now on the hunt for their ninth permanent manager or head coach in four years outside the English Football League, following the takeover by American businessman Landon Smith in January.