Albion have now won just one of their last five homes games - taking five points from a possible 15.
They had enough chances to have raced to a comfortable victory only to be let down by their finishing and the form of Reading's central defenders Ivar Ingimarsson and Ricky Newman.
Albion's leading scorer Rob Hulse had a particularly frustrating night - missing a host of chances.
While Albion were disappointed, the point extended Reading's good run under new boss Steve Coppell.
The Royals have now lost just twice in nine games since Coppell took charge at the Madjeski Stadium.
Jason Koumas proved a constant thorn in Reading's side in the first half but could not inspire Albion to the breakthrough that their pressure deserved.
The Welsh international tested Reading goalkeeper Marcus Hahnemann with a long-range chip in the 23rd minute and then turned provider for Andy Johnson five minutes later.
Koumas swung over a corner that picked out the unmarked Johnson just six yards from goal.
Johnson should have buried the chance but he headed the ball into the ground and saw it loop over the crossbar.
Reading struggled to make much of an impact in attack themselves in the first half and all they had to show for their efforts was a 20-yard drive from Graeme Murty that whistled just wide ten minutes before the interval.
Albion's pressure then finally looked set to pay-off on the stroke of half-time through Hulse.
He gained possession after the ball bounced off his team-mate, Paul Robinson, only to see his shot well held by Hahnemann.
Reading continued to ride their luck in the second half as Albion's finishing once again let them down.
Twice within the space of two minutes they spurned clear-cut chances.
First Hulse miskicked completely from six yards in the 57th minute before full-back Bernt Haas blazed over the bar just eight yards out.
Reading were content to try and pick Albion off on the break and it almost worked 15 minutes from time when winger John Salako saw his shot fly just wide.
Hulse's dismal evening was then perfectly summed up in injury time as he headed over the bar from four yards to leave Albion reflecting on what might have been.