The Shots were the better side in a first half which saw the visitors pose plenty of questions towards the latter stages as the Dale limped in at the interval fortunate to keep their clean sheet intact.
Yet striker George Donnelly handed the hosts the initiative with a 52nd-minute opener, collecting Michael Rose's throughball and slipping a neat finish past Jamie Young.
But Aldershot hit back when Adam Mekki capitalised on a slip from goalkeeper Josh Lillis, who spilled Ben Herd's free-kick straight to the substitute. Asa Hall then almost compounded Dale's disappointment when he struck the woodwork from distance.
"I do not know how we haven't won that," said Scott afterwards. "I would go as far as saying it's our best performance since I have been in charge.
"Their 'keeper made three fantastic saves and I don't know how we have only scored one goal. We went 1-0 down but we recovered well and should have won the game but it's ifs and buts and we have got to move on now.
"Our Achilles heel has been scoring this season and it showed again as we had plenty of chances.
"But we gave our all on the pitch and if we play like that we will win games. We have got to keep believing."