The lack of finishing cost them dearly with Darren Wrack their main culprit when he headed wide of an open goal in the second half.
Orient defended in depth and certainly put the Saddlers out of their stride to pick up another vital away point to keep themselves in touch with the play-off zone.
Although both teams produced spells of good football in the first half, neither side could find the cutting edge to dominate the match.
The closest Walsall came to opening their account in this period came in the 32nd minute when on-loan Lee Holmes fired in a blistering long-range shot which goalkeeper Stuart Nelson saved cleanly.
Veteran striker Tommy Mooney worked hard to set up his young colleagues, but despite some deft touches the Saddlers were unable to break through a defence in which Brian Saah and Tamika Mkandawire handled any dangerous situation with calm authority.
Very little, however, was seen of Orient's top-scorer Adam Boyd, who had few opportunities to add to his nine-goal haul.
In the second half, Walsall produced more positive play and Edrissa Sonko, who had scored in the previous two games, carelessly shot wide after a smart move involving Holmes and Mooney.
Orient were indebted to a brave save by Nelson who dived at the feet of Mooney to cut out a cross from Alex Nicholls.
The goalkeeper then earned the first yellow card for kicking the ball onto the roof of the stand in a time wasting move.
Orient had a 62nd minute let-off when Wrack inexplicably headed wide.
Nicholls produced a determined run across field and laid on a pass for Holmes to cross to the far post where Wrack conspired to miss a golden opportunity.