Parslow started 2013–14 in and out of the team, but when returning to the starting line-up for a 2–1 home defeat to Mansfield Town on 14 September 2013 was handed the captain's armband in the absence of Smith. He established himself in the centre of defence alongside McGurk, and retained the armband when Smith was recalled into the team. However, he sustained knee ligament damage when colliding into advertising hoardings as he sliced an attempted clearance during York's 2–1 defeat away to Southend on 23 November 2013. The injury ruled him out for the rest of the season, in which he had made 16 appearances. In his absence, York reached the play-offs with a seventh-place finish in League Two, although they were beaten 1–0 on aggregate by Fleetwood Town in the semi-final.