Failure to make the League Two play-offs this season has seen chairman Paul Scally take action, although Hessenthaler, a Gillingham hero from previous spells as player and manager, has been offered a place on the club's board.
A 1-1 draw at Sixfields against Northampton in the penultimate game of the season meant the play-offs were out of reach, after which Hessenthaler told BBC Radio Kent: "I love this club.
"It's in my blood and I'm hurting just as much as the fans, the chairman and the board of directors are.
"Hopefully I'll get time to rebuild in the summer, go again and achieve it next year.
"I couldn't give any more hours to the club and the chairman knows that."