Orient came into the game depleted by injuries, with Dean Cox the latest to be sidelined for the Londoners.
The O's, showing little sign of their indifferent start to the season, had another chance on 17 minutes when the ball fell to Shaun Batt, but his strike was well off target.
Randall then found himself in space moments later, but his strike from the edge of the area was wayward.
Orient then enjoyed their best opportunities of the first period when first Jay Simpson had his close-range header blocked just after the half-hour mark, before Shane Lowry brought another save out of Martin.
The ex-Liverpool keeper was called into action again on 36 minutes as he saved a low strike from Batt.