York failed to score for their fourth consecutive home game as play-off chasing Southend left Bootham Crescent with a point.
Ryan Bowman forced Daniel Bentley into a low save and Michael Coulson and Will Hayhurst also went close for the hosts.
Kevan Hurst fired the visitors' best chance of the first half wide, while Barry Corr sent two headers off target.
Coulson came close to winning it for the Minstermen late on but his effort was blocked on the line.
York City manager Nigel Worthington told BBC Radio York:
"They're not easy to win. Like the Cheltenham game you're playing against a decent team who have been in the league for a long time.
"It's never an easy situation but I can't really fault the players.
"I thought some of the play at times was very good, the commitment and work ethic was high quality.
"So at home maybe we need just that rub of the green to take us over the line, but the important thing is that we are working at it and towards it so that's a good thing."
York City 31 Pope 02 Oyebanjo 03 Davies Booked 10 Penn 15 Lowe 16 McCombe 12 Carson 37 Reed 19 Bowman Booked (Jarvis - 71' ) 07 Coulson (Dickinson - 91' ) 26 Hayhurst Substitutes 05 McGurk 11 Jarvis 14 Montrose 18 Platt 24 Ingham 25 Dickinson 28 Puri Southend United 17 Bentley 02 White 03 Coker 12 Atkinson 15 Bolger (Phillips - 79' ) 23 Thompson 14 Hurst 18 Leonard 10 Corr Booked 08 Timlin (Payne - 56' ) 11 Straker (Laird - 75' ) Substitutes 01 Smith 04 Laird 05 Phillips 07 Eastwood 21 Payne 28 Williams 29 Gomis
Ref: Paul Tierney