Chances were limited for both sides throughout the game, Kevan Hurst going closest for the Shrimpers in the first half with his effort going narrowly wide of the target.
Southend are now without a win in six league games and Brown feels they need to improve in the final third to get back on a winning run.
"I'm delighted with the clean sheet and it is (goalkeeper) Dan Bentley's 13th of the season, so I'm very pleased for the young lad," he said.
"I just felt we didn't really do enough once again in the final third. We looked solid as a back four but York didn't really create too many chances. However, we are disappointed that we didn't put our best foot forward when we had the ball.
"You can make excuses about the surface but it was a better game than here last season when the ball was in the air for 75% of the time.
"We did try to play but York worked hard against us and I was just disappointed that we didn't create enough. We had chances to get a goal through Barry Corr's header but we just didn't have the quality with the ball."
- Sports & Recreation
- Kevan Hurst