The Shrimpers threatened in the closing stages of the first half with Kevan Hurst shooting narrowly wide before Nick Pope had to stop Lanre Oyebanjo from inadvertently diverting the ball into his own net.
That elusive first goal nearly came after 60 minutes, Southend's Barry Corr heading over from John White's delivery before nodding wide of the target shortly after.
However, it was York who came closest to winning the game in the closing stages with Coulson bursting into the area only for Thompson to block his effort on the line as it finished all square.
- Michael Coulson
- Adam Thompson
- Ryan Bowman
- Daniel Bentley