An own goal gave the Rebels a first half lead and that was how it stayed until Gosport punished a tired-looking home side with the equaliser four minutes into injury time.
The Rebles then missed three spot-kicks in the shootout to lose 3-2 and miss out on a spot in the last 32.
See pictures by Kyle Hemsley on this page and the ones linked – and get the latest from Woodside Road in the Herald, out on Thursday, and on this website during the week
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