Despite hitting national headlines with their FA Cup run, knocking Premiership giants Everton out of the prestigious competition, Ratcliffe accepted the blame for the relegation with a game to spare.
He said: "I am responsible for the team and 90 per cent of the players that are here are my players.
"However painful it is for me, I feel I have no other option than to resign from my post as manager.
"The buck stops with me. I've brought in the players, I've picked the team but at the end of the day we haven't been good enough over the season."
Former Scunthorpe United midfielder Mark Atkins will be in charge of the Shrews on Saturday alongside youth team coach Nigel Vaughan.