The Robins' new signing from Huddersfield took the penalty in the 71st minute, awarded after a handball in the Pools penalty area by Peter Hartley, but he lacked composure and his right-footed kick was blazed high over the roof of the stand.
Paolo Di Canio's side had the better chances and looked the most likely to score in a competitive and entertaining encounter.
Miller had the game's first chance after five minutes, shooting straight at goalkeeper Scott Flinders from 20 yards.
Flinders then saved well from Matt Richie after the winger had been picked out at the far post by Raffaele De Vita on the opposite flank.
A heavy touch by Pools' James Poole in the area cost him a chance, but a minute later the home side almost snatched the lead when Evan Horwood's free-kick was met by Steve Howard and the striker's header came back off the post with goalkeeper Wes Foderingham beaten.