Aldershot created the better chances of the first half, with Southend goalkeeper Glenn Morris denying Jermaine McGlashan and former Blues midfielder Luke Guttridge.
And the Shots might have gone in at half-time in the lead but Morris parried Damien Spencer's close-range effort, before Bilel Moshni headed Guttridge's follow-up clear in stoppage time.
Guttridge was denied by Morris just after the break before Kane Ferdinand released Corr but his lob went over the bar having beaten Shots goalkeeper Jamie Young.
Southend registered their first effort on target when Anthony Grant rifled a fine shot towards the top right corner, which was turned out by Young.
At the other end of the pitch Spencer's header was parried onto his left post by Morris, before the crossbar came to Shots' rescue after Corr's effort had beaten Young. Guttridge flashed a free-kick wide of the right upright in the closing action of the match.
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