Both sides struggled to create clear-cut chances during a dire game and there was little to entertain the supporters.
However, York could have opened the scoring in the 54th minute when an unmarked Jason Walker headed Matty Blair's right-wing cross wide of the left post from six yards.
Two minutes later Blair raced through on goal but the winger was denied by a fine double save from Shrimpers goalkeeper Paul Smith.
Southend got more in to the game late on and could have snatched the win in the dying minutes. Captain Chris Barker headed over from close range after Kevan Hurst's free-kick had been flicked on by Britt Assombalonga.
And, in the very last minute, Hurst sent a poor half-volley over the crossbar from eight yards after Sean Clohessy's right wing crossed had been knocked down in to his path.