County, founded in 1862, needed to beat Swindon and Macclesfield Town lose at home to Cambridge United to ensure they prolonged their stay in the Football League.
At one point, a great escape looked on as County took the lead at Swindon and Macclesfield trailed Cambridge with 65 minutes gone.
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But moments after Macclesfield equalised, County were pegged back and they conceded two more goals to seal their relegation to the fifth tier of English football for the first time in their history.
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