The Robins hit back from two goals down to clinch a point in sharp contrast to Saturday's game when they led Woking 2-0 after only 18 minutes only to eventually lose 3-2.
In a tempestuous game of five bookings, the visitors also had manager Graham Heathcote sent off.
Forest Green took the lead in the sixth minute when new signing Adriano Rigoglioso scored with a neat finish and they looked set to clinch a rare three-point haul when Simon Clist slammed the ball home from close range ten minutes before the interval.
However, seven minutes into the second half, Sam Thornley halved the deficit and, before the hour, Altrincham were level when Kieran Lugsden turned Colin Potts' right-wing cross home.
Rovers remain one off the foot of the table thanks to Crawley's ten-point deduction but have now drawn four and lost six of their opening ten Conference games.
Altrincham are 17th with ten points, and the New Lawn clash was the first they have not lost in five games away from Moss Road this season.