York City lost further ground on league leaders Wrexham after playing out a goalless draw at Barrow in which they had two men sent off in injury time.
The Bluebirds nearly took the lead when Richie Baker fired in a free-kick, but keeper Michael Ingham saved well.
Jason Walker's free-kick for York then saw Danny Hurst tip over the bar and Baker fired just wide for the hosts.
Walker was then sent off for a foul on James Owen and team-mate Andre Boucard was dismissed in the subsequent melee.
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York City manager Gary Mills told BBC Radio York:
"All I ask is consistency from referees. We all do every week. Jason's challenge looked to me a nasty challenge which I'd like to see again.
"It looked straight legged so until I see it again I've got no argument with Jason going off.
"With Andre, to pick one person out of that melee is beyond me. I'm going to go and see the referee and ask a few questions."