The game's crucial moments came when Michael Welch appeared to push an Altrincham defender on the byline before looping a hopeful header goalwards.
Stuart Coburn was clearly distracted by a heavy challenge from Andrew Mangan and the Robins keeper couldn't keep the ball out with his flailing right hand.
Altrincham had the better of the first half after John Coleman's men dominated the opening exchanges. Gary Williams stung the hands of Stuart Jones following a smart turn inside the area and Colin Little missed the first of a host of opportunities, failing to convert and excellent Colin Potts cross.
The former Crewe man rattled the inside of the post after the Lancashire side failed to deal with a long throw from the impressive Lewis Chalmers and it was Little again denied by a fine reaction save by Jones before blazing the rebound across the face of the goal.
Former Altrincham maestro Ian Craney went very close early in the second half, before a Chalmers header created a great opening for the hapless Little, who again failed to find the target.
Altrincham powered forward throughout the second half and Peter Band released Little over the top of a square Stanley defence, but the Robins marksman's effort was too close to Jones.
And even after the crucial goal had arrived there was one final opportunity for the man who scored 38 times for the Robins last season, as he combined well with substitute Nehru McKenzie, but saw his low shot smothered by Jones at the second attempt.
While Altrincham manager Graham Heathcote will undoubtedly be disappointed not to have taken at least a point, he will have been very encouraged by the excellent display his team gave him following Saturday's 3-0 drubbing at Stevenage.