The game was called off just over an hour before kick-off, meaning the long journey to Devon was a fruitless one for Chris Hogg and his players.
The fixture will now be rearranged, with a place in the quarter-finals at stake. Newcastle reached the final last season, losing 1-0 to Everton at Goodison Park.
Details of the new date will be announced on nufc.co.uk in due course.