Andrews, 34, had previously called it a day following a spell at Bury Town only to be lured back by Rangers boss Fallon, who he played under for many years at Histon.
Fallon said: “He has got other things to concentrate on and they've got a little one on the way in August as well, so that was his last game.
He did me a big favour to play again this year because players can learn from the example he sets because he’s a winner and he goes about things properly. He made Soham a better team because we needed to sort out one or two things such as attitudes towards the game.
Neil’s the perfect example of how to conduct yourself and that rubbed off on everyone else. He could have played for another year or two, but it’s his decision and he feels it’s time to move on.”