Both sides gave their all in poor conditions at Victoria Park without finding a route to goal.
The point sees the Glovers drop to fifth in League One, while Pools are now six short of safety in the relegation zone.
Pools have now lost only once in nine, but have suffered two frustrating 0-0 draws at home in the last week to leave them six points adrift of Scunthorpe, the team directly above the drop zone.
"There's frustration from the outcome," said boss John Hughes. "But we were up against a good side, at this stage of the season we need three points.
"What they have achieved since Christmas has been commendable. Anyone watching can see there is a fight to it, if we are going down, go down having a fight.
"The teams we are chasing have all lost - it might be two dropped, it might be one towards safety. If it goes to the end of the season and the last game, so be it. Bring it on."
Pools had a late chance to win it when substitute Antony Sweeney was played in on goal, but he pushed his shot too close to Glovers goalkeeper Marek Stech.
Hughes added: "Keep that back door shut and you have a chance. We had the best chance of the second half after keeping that back door shut.
"We kept a clean sheet and it's spirited. Who knows, we may win the next three games and all is well."