The Highwaymen have endured a difficult start to the Northern Premier League season, and sit bottom of the Premier Division with four points from nine games.
Turnbull offered his resignation to chairman Ken Beattie following the 2-1 defeat to Witton on Saturday.
Beattie said: “I’ve got the greatest respect and regard for Stephen and he has been extremely unlucky with a number of factors including Covid-related disruption.
“He has been a tremendous player and ambassador for Morpeth Town. He has high standards and will continue to do well going forward.”
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