The point leaves the Bees three shy of the top six, with four games to play.
There were few real openings throughout and, in the first 45 minutes, Scott Flinders went down low to his right to keep out an angled drive from Clayton Donaldson.
Pools were brighter for the 56th-minute introduction of substitute Luke James, who injected some life into their attack. And they thought they had ended their recent goal drought after 66 minutes. After keeper Richard Lee kept out a close-range effort, a minute later he was beaten.
James shot from distance took a deflection on the way into the net via a visiting defender, an offside flag was raised.
Toumani Diagouraga should have won it for the Bees after 77 minutes. Clinton Morrison broke down the right and rolled the ball across the edge of the penalty area only for the midfielder to horribly push wide from six yards.