The Shots were celebrating a return to the league following a 16-year absence and Scott Donnelly was their hero curling home an 18-yard free kick into the top corner of the net on 43 minutes.
The Reds - who lost 15 of their home games last season - were left to rue the chances which got away with Paul Mullin breaking clean through but having his effort saved by keeper Nikki Bull and the Shots stopper also kept out an Andy Procter header.
"Our delivery was poor, our set pieces weren't good enough and our finishing was diabolical," said Stanley manager John Coleman.
"We had made a conscious effort to try and improve our home form but it didn't happen. It is disappointing.
"We won the first half on points but were 1-0 down and if you bring people down on the edge of the area and concede a free kick then you are always going to run the risk of conceding goals.
"We had enough chances to win two games but we have had a problem scoring goals and if it continues, I may have to bring in another striker."
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